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139 publications using GAP in the category "Nonassociative rings and algebras"

[AA+21] Ali, S., Azad, H., Biswas, I., and de Graaf, W. A., A constructive method for decomposing real representations, J. Symbolic Comput., 104 (2021), 328–342.

[A19] Amicone, F., Classification of balanced toral elements of exceptional Lie algebras, J. Algebra, 524 (2019), 395–419.

[AS20] Angiono, I. and Sanmarco, G., Pointed Hopf algebras over non abelian groups with decomposable braidings, I, J. Algebra, 549 (2020), 78–111.

[AJM10] Avitabile, M., Jurman, G., and Mattarei, S., The structure of thin Lie algebras with characteristic two, Internat. J. Algebra Comput., 20 (6) (2010), 731–768.

[AM05] Avitabile, M. and Mattarei, S., Thin Lie algebras with diamonds of finite and infinite type, J. Algebra, 293 (1) (2005), 34–64.

[BR18] Bagarello, F. and Russo, F. G., A description of pseudo-bosons in terms of nilpotent Lie algebras, J. Geom. Phys., 125 (2018), 1–11.

[BR20] Bagarello, F. and Russo, F. G., Realization of Lie algebras of high dimension via pseudo-bosonic operators, J. Lie Theory, 30 (4) (2020), 925–938.

[B04] Bartholdi, L., The 2-dimension series of the just-nonsolvable BSV group, New Zealand J. Math., 33 (1) (2004), 17–23.

[B05] Bartholdi, L., Lie algebras and growth in branch groups, Pacific J. Math., 218 (2) (2005), 241–282.

[B06] Bartholdi, L., Branch rings, thinned rings, tree enveloping rings, Israel J. Math., 154 (2006), 93–139.

[BE+06] Bartholdi, L., Enriquez, B., Etingof, P., and Rains, E., Groups and Lie algebras corresponding to the Yang-Baxter equations, J. Algebra, 305 (2) (2006), 742–764.

[BG+17] Baumeister, B., Gobet, T., Roberts, K., and Wegener, P., On the Hurwitz action in finite Coxeter groups, J. Group Theory, 20 (1) (2017), 103–131.

[BN+11] Beites, P. D., Nicolás, A. P., Pozhidaev, A. P., and Saraiva, P., On identities of a ternary quaternion algebra, Comm. Algebra, 39 (3) (2011), 830–842.

[BN+20] Bendel, C. P., Nakano, D. K., Pillen, C., and Sobaje, P., Counterexamples to the tilting and $(p,r)$-filtration conjectures, J. Reine Angew. Math., 767 (2020), 193–202.

[BJT20] Bocheński, M., Jastrz\cebski, P., and Tralle, A., Nonexistence of standard compact Clifford-Klein forms of homogeneous spaces of exceptional Lie groups, Math. Comp., 89 (323) (2020), 1487–1499.

[BG18] Brown, J. and Goodwin, S. M., On the variety of 1-dimensional representations of finite $W$-algebras in low rank, J. Algebra, 511 (2018), 499–515.

[BG07] Brundan, J. and Goodwin, S. M., Good grading polytopes, Proc. Lond. Math. Soc. (3), 94 (1) (2007), 155–180.

[B11] Bulois, M., Irregular locus of the commuting variety of reductive symmetric Lie algebras and rigid pairs, Transform. Groups, 16 (4) (2011), 1027–1061.

[B18] Bulois, M., On the normality of the null-fiber of the moment map for $\theta$- and tori representations, J. Algebra, 507 (2018), 502–524.

[BH16] Bulois, M. and Hivert, P., Sheets in symmetric Lie algebras and slice induction, Transform. Groups, 21 (2) (2016), 355–375.

[BEG09] Burde, D., Eick, B., and de Graaf, W., Computing faithful representations for nilpotent Lie algebras, J. Algebra, 322 (3) (2009), 602–612.

[C97] Caranti, A., Presenting the graded Lie algebra associated to the Nottingham group, J. Algebra, 198 (1) (1997), 266–289.

[CJ99] Caranti, A. and Jurman, G., Quotients of maximal class of thin Lie algebras. The odd characteristic case, Comm. Algebra, 27 (12) (1999), 5741–5748.

[CM04] Caranti, A. and Mattarei, S., Nottingham Lie algebras with diamonds of finite type, Internat. J. Algebra Comput., 14 (1) (2004), 35–67.

[CMN97] Caranti, A., Mattarei, S., and Newman, M. F., Graded Lie algebras of maximal class, Trans. Amer. Math. Soc., 349 (10) (1997), 4021–4051.

[C18] Carnahan, S., 51 constructions of the Moonshine module, Commun. Number Theory Phys., 12 (2) (2018), 305–334.

[C19] Carnahan, S., A self-dual integral form of the Moonshine module, SIGMA Symmetry Integrability Geom. Methods Appl., 15 (2019), Paper No. 030, 36.

[C01] Carrara, C., (Finite) presentations of the Albert-Frank-Shalev Lie algebras, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), 4 (2) (2001), 391–427.

[CG09] Cicalò, S. and de Graaf, W. A., Non-associative Gröbner bases, finitely-presented Lie rings and the Engel condition. II, J. Symbolic Comput., 44 (7) (2009), 786–800.

[CGS12] Cicalò, S., de Graaf, W. A., and Schneider, C., Six-dimensional nilpotent Lie algebras, Linear Algebra Appl., 436 (1) (2012), 163–189.

[CGV12] Cicalò, S., de Graaf, W. A., and Vaughan-Lee, M., An effective version of the Lazard correspondence, J. Algebra, 352 (2012), 430–450.

[CGR97] Cohen, A. M., de Graaf, W. A., and Rónyai, L., Computations in finite-dimensional Lie algebras, Discrete Math. Theor. Comput. Sci., 1 (1) (1997), 129–138
(Lie computations (Marseille, 1994)).

[CGW14] Cohen, A. M., Gijsbers, D. A. H., and Wales, D. B., The Birman-Murakami-Wenzl algebras of type $D_n$, Comm. Algebra, 42 (1) (2014), 22–55.

[CIR08] Cohen, A. M., Ivanyos, G., and Roozemond, D., Simple Lie algebras having extremal elements, Indag. Math. (N.S.), 19 (2) (2008), 177–188.

[CR09] Cohen, A. M. and Roozemond, D., Computing Chevalley bases in small characteristics, J. Algebra, 322 (3) (2009), 703–721.

[CS+01] Cohen, A. M., Steinbach, A., Ushirobira, R., and Wales, D., Lie algebras generated by extremal elements, J. Algebra, 236 (1) (2001), 122–154.

[CW11] Cohen, A. M. and Wales, D. B., The Birman-Murakami-Wenzl algebras of type $\bold E_n$, Transform. Groups, 16 (3) (2011), 681–715.

[CH18] Cook, W. J. and Hughes, N. A., On the minuscule representation of type $B_n$, Involve, 11 (5) (2018), 721–733.

[CH+12] Cuypers, H., Horn, M., in 't panhuis, J., and Shpectorov, S., Lie algebras and 3-transpositions, J. Algebra, 368 (2012), 21–39.

[G97] de Graaf, W. A., Constructing faithful matrix representations of Lie algebras, in Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation (Kihei, HI), ACM, New York (1997), 54–59.

[G99] de Graaf, W. A., Using Cartan subalgebras to calculate nilradicals and Levi subalgebras of Lie algebras, J. Pure Appl. Algebra, 139 (1-3) (1999), 25–39
(Effective methods in algebraic geometry (Saint-Malo, 1998)).

[G00] de Graaf, W. A., Lie algebras: theory and algorithms, North-Holland Publishing Co., Amsterdam, North-Holland Mathematical Library, 56 (2000), xii+393 pages.

[G01] de Graaf, W. A., Computing with quantized enveloping algebras: PBW-type bases, highest-weight modules and $R$-matrices, J. Symbolic Comput., 32 (5) (2001), 475–490.

[G01] de Graaf, W. A., Constructing representations of split semisimple Lie algebras, J. Pure Appl. Algebra, 164 (1-2) (2001), 87–107
(Effective methods in algebraic geometry (Bath, 2000)).

[G02] de Graaf, W. A., Constructing canonical bases of quantized enveloping algebras, Experiment. Math., 11 (2) (2002), 161–170.

[G03] de Graaf, W. A., An algorithm to compute the canonical basis of an irreducible module over a quantized enveloping algebra, LMS J. Comput. Math., 6 (2003), 105–118.

[G05] de Graaf, W. A., Constructing homomorphisms between Verma modules, J. Lie Theory, 15 (2) (2005), 415–428.

[G07] de Graaf, W. A., Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2, J. Algebra, 309 (2) (2007), 640–653.

[G11] de Graaf, W. A., Computing representatives of nilpotent orbits of $\theta$-groups, J. Symbolic Comput., 46 (4) (2011), 438–458.

[G11] de Graaf, W. A., Constructing semisimple subalgebras of semisimple Lie algebras, J. Algebra, 325 (2011), 416–430.

[GE09] de Graaf, W. A. and Elashvili, A., Induced nilpotent orbits of the simple Lie algebras of exceptional type, Georgian Math. J., 16 (2) (2009), 257–278.

[GM20] de Graaf, W. A. and Marrani, A., Real forms of embeddings of maximal reductive subalgebras of the complex simple Lie algebras of rank up to 8, J. Phys. A, 53 (15) (2020), 155203, 13.

[GVY12] de Graaf, W. A., Vinberg, E. B., and Yakimova, O. S., An effective method to compute closure ordering for nilpotent orbits of $\theta$-representations, J. Algebra, 371 (2012), 38–62.

[GW99] de Graaf, W. A. and Wisliceny, J., Constructing bases of finitely presented Lie algebras using Gröbner bases in free algebras, in Proceedings of the 1999 International Symposium on Symbolic and Algebraic Computation (Vancouver, BC), ACM, New York (1999), 37–43.

[GY12] de Graaf, W. A. and Yakimova, O. S., Good index behaviour of $\theta$-representations, I, Algebr. Represent. Theory, 15 (4) (2012), 613–638.

[DIR96] De Graaf, W., Ivanyos, G., and Rónyai, L., Computing Cartan subalgebras of Lie algebras, Appl. Algebra Engrg. Comm. Comput., 7 (5) (1996), 339–349.

[M19] de Mendonça, L. A., The weak commutativity construction for Lie algebras, J. Algebra, 529 (2019), 145–173.

[M20] de Mendonça, L. A., Weak commutativity and nilpotency, J. Algebra, 564 (2020), 276–299.

[D14] Decelle, S., The $L_2(11)$-subalgebra of the Monster algebra, Ars Math. Contemp., 7 (1) (2014), 83–103.

[DG13] Dietrich, H. and de Graaf, W. A., A computational approach to the Kostant-Sekiguchi correspondence, Pacific J. Math., 265 (2) (2013), 349–379.

[DG21] Dietrich, H. and de Graaf, W. A., Computing the real Weyl group, J. Symbolic Comput., 104 (2021), 1–14.

[DFG13] Dietrich, H., Faccin, P., and de Graaf, W. A., Computing with real Lie algebras: real forms, Cartan decompositions, and Cartan subalgebras, J. Symbolic Comput., 56 (2013), 27–45.

[DFG15] Dietrich, H., Faccin, P., and de Graaf, W. A., Regular subalgebras and nilpotent orbits of real graded Lie algebras, J. Algebra, 423 (2015), 1044–1079.

[DGH98] Dong, C., Griess Jr. , R. L., and Höhn, G., Framed vertex operator algebras, codes and the Moonshine module, Comm. Math. Phys., 193 (2) (1998), 407–448.

[DG21] Douglas, A. and de Graaf, W. A., Closed subsets of root systems and regular subalgebras, J. Algebra, 565 (2021), 531–547.

[DGR13] Douglas, A., de Guise, H., and Repka, J., The Poincaré algebra in rank 3 simple Lie algebras, J. Math. Phys., 54 (2) (2013), 023508, 18.

[DJR11] Douglas, A., Joseph, W., and Repka, J., A classification of the embeddings of the Diamond Lie algebra into $\germsl(3,\Bbb C)$ and $\germsp(4,\Bbb C)$ and restrictions of irreducible modules, J. Math. Phys., 52 (10) (2011), 103507, 10.

[DKR13] Douglas, A., Kahrobaei, D., and Repka, J., Classification of embeddings of abelian extensions of $D_n$ into $E_n+1$, J. Pure Appl. Algebra, 217 (10) (2013), 1942–1954.

[DR11] Douglas, A. and Repka, J., Indecomposable representations of the Euclidean algebra $\germ e(3)$ from irreducible representations of $\germsl(4,\Bbb C)$, Bull. Aust. Math. Soc., 83 (3) (2011), 439–449.

[DR14] Douglas, A. and Repka, J., The GraviGUT algebra is not a subalgebra of $E_8$, but $E_8$ does contain an extended GraviCUT algebra, SIGMA Symmetry Integrability Geom. Methods Appl., 10 (2014), Paper 072, 10.

[DR15] Douglas, A. and Repka, J., Levi decomposable algebras in the classical Lie algebras, J. Algebra, 428 (2015), 292–314.

[DR15] Douglas, A. and Repka, J., Levi decomposable subalgebras of the symplectic algebra $C_2$, J. Math. Phys., 56 (5) (2015), 051703, 10.

[DR16] Douglas, A. and Repka, J., The subalgebras of $A_2$, J. Pure Appl. Algebra, 220 (6) (2016), 2389–2413.

[DR16] Douglas, A. and Repka, J., The subalgebras of $\germ so(4,\Bbb C)$, Comm. Algebra, 44 (12) (2016), 5269–5286.

[DR17] Douglas, A. and Repka, J., The subalgebras of the rank two symplectic Lie algebra, Linear Algebra Appl., 527 (2017), 303–348.

[DR18] Douglas, A. and Repka, J., Subalgebras of the rank two semisimple Lie algebras, Linear Multilinear Algebra, 66 (10) (2018), 2049–2075.

[D01] Draisma, J., Recognizing the symmetry type of O.D.E.s, J. Pure Appl. Algebra, 164 (1-2) (2001), 109–128
(Effective methods in algebraic geometry (Bath, 2000)).

[D02] Draisma, J., On a conjecture of Sophus Lie, in Differential equations and the Stokes phenomenon, World Sci. Publ., River Edge, NJ (2002), 65–87.

[D03] Draisma, J., Constructing Lie algebras of first order differential operators, J. Symbolic Comput., 36 (5) (2003), 685–698.

[D06] Draisma, J., Small maximal spaces of non-invertible matrices, Bull. London Math. Soc., 38 (5) (2006), 764–776.

[D12] Draisma, J., Transitive Lie algebras of vector fields: an overview, Qual. Theory Dyn. Syst., 11 (1) (2012), 39–60.

[D11] Drupieski, C. M., On injective modules and support varieties for the small quantum group, Int. Math. Res. Not. IMRN (10) (2011), 2263–2294.

[DZ10] Dzhumadilʹdaev, A. and Zusmanovich, P., Commutative 2-cocycles on Lie algebras, J. Algebra, 324 (4) (2010), 732–748.

[E04] Eick, B., Computing the automorphism group of a solvable Lie algebra, Linear Algebra Appl., 382 (2004), 195–209.

[EG21] Eick, B. and Ghorbanzadeh, T. J., Computing the Schur multipliers of the Lie $p$-rings in the family defined by a symbolic Lie $p$-ring presentation, J. Symbolic Comput., 106 (2021), 68–77.

[EV20] Eick, B. and Vaughan-Lee, M., Counting $p$-groups and Lie algebras using PORC formulae, J. Algebra, 545 (2020), 198–212.

[EKV13] Elashvili, A. G., Kac, V. G., and Vinberg, E. B., Cyclic elements in semisimple Lie algebras, Transform. Groups, 18 (1) (2013), 97–130.

[EMT10] Ellis, G., Mohammadzadeh, H., and Tavallaee, H., Computing covers of Lie algebras, in Computational group theory and the theory of groups, II, Amer. Math. Soc., Providence, RI, Contemp. Math., 511 (2010), 25–31.

[FG15] Faccin, P. and de Graaf, W. A., Constructing semisimple subalgebras of real semisimple Lie algebras, in Lie algebras and related topics, Amer. Math. Soc., Providence, RI, Contemp. Math., 652 (2015), 75–89.

[FG11] Fortunato, L. and de Graaf, W. A., Angular momentum non-conserving symmetries in bosonic models, J. Phys. A, 44 (14) (2011), 145206, 12.

[FR08] Fowler, R. and Röhrle, G., Spherical nilpotent orbits in positive characteristic, Pacific J. Math., 237 (2) (2008), 241–286.

[FIM16] Franchi, C., Ivanov, A. A., and Mainardis, M., The $2A$-Majorana representations of the Harada-Norton group, Ars Math. Contemp., 11 (1) (2016), 175–187.

[G16] Gannon, T., Much ado about Mathieu, Adv. Math., 301 (2016), 322–358.

[G00] Ginzburg, V., Principal nilpotent pairs in a semisimple Lie algebra. I, Invent. Math., 140 (3) (2000), 511–561.

[G05] Goodwin, S., Algorithmic testing for dense orbits of Borel subgroups, J. Pure Appl. Algebra, 197 (1-3) (2005), 171–181.

[G05] Goodwin, S. M., Relative Springer isomorphisms, J. Algebra, 290 (1) (2005), 266–281.

[GRU10] Goodwin, S. M., Röhrle, G., and Ubly, G., On 1-dimensional representations of finite $W$-algebras associated to simple Lie algebras of exceptional type, LMS J. Comput. Math., 13 (2010), 357–369.

[GS20] Gorshkov, I. and Staroletov, A., On primitive 3-generated axial algebras of Jordan type, J. Algebra, 563 (2020), 74–99.

[G11] Grabowski, J. E., Braided enveloping algebras associated to quantum parabolic subalgebras, Comm. Algebra, 39 (10) (2011), 3491–3514.

[G11] Grabowski, J. E., Examples of quantum cluster algebras associated to partial flag varieties, J. Pure Appl. Algebra, 215 (7) (2011), 1582–1595.

[GZ17] Grishkov, A. and Zusmanovich, P., Deformations of current Lie algebras. I. Small algebras in characteristic 2, J. Algebra, 473 (2017), 513–544.

[G99] Groves, D., A note on nonidentical Lie relators, J. Algebra, 211 (1) (1999), 15–25.

[HS16] Herpel, S. and Stewart, D. I., Maximal subalgebras of Cartan type in the exceptional Lie algebras, Selecta Math. (N.S.), 22 (2) (2016), 765–799.

[HRW08] Hong, S., Rowell, E., and Wang, Z., On exotic modular tensor categories, Commun. Contemp. Math., 10 (suppl. 1) (2008), 1049–1074.

[iPR09] in 't panhuis, J., Postma, E., and Roozemond, D., Extremal presentations for classical Lie algebras, J. Algebra, 322 (2) (2009), 295–326.

[IS12] Ivanov, A. A. and Seress, Á., Majorana representations of $A_5$, Math. Z., 272 (1-2) (2012), 269–295.

[IS12] Ivanov, A. A. and Shpectorov, S., Majorana representations of $L_3(2)$, Adv. Geom., 12 (4) (2012), 717–738.

[JS20] Jensen, B. T. and Su, X., Existence of Richardson elements for seaweed Lie algebras of finite type, J. Lond. Math. Soc. (2), 101 (2) (2020), 505–529.

[J04] Jurman, G., A family of simple Lie algebras in characteristic two, J. Algebra, 271 (2) (2004), 454–481.

[J05] Jurman, G., Graded Lie algebras of maximal class. III, J. Algebra, 284 (2) (2005), 435–461.

[KZ21] Kaygorodov, I. and Zusmanovich, P., On anticommutative algebras for which $[R_a, R_b]$ is a derivation, J. Geom. Phys., 163 (2021), 104113, 10.

[KPS13] Kochetov, M., Parsons, N., and Sadov, S., Counting fine grading on matrix algebras and on classical simple Lie algebras, Internat. J. Algebra Comput., 23 (7) (2013), 1755–1781.

[KP11] Kolb, S. and Pellegrini, J., Braid group actions on coideal subalgebras of quantized enveloping algebras, J. Algebra, 336 (2011), 395–416.

[LMR17] López Peña, J., Majid, S., and Rietsch, K., Lie theory of finite simple groups and the Roth property, Math. Proc. Cambridge Philos. Soc., 163 (2) (2017), 301–340.

[MZ18] Makhlouf, A. and Zusmanovich, P., Hom-Lie structures on Kac-Moody algebras, J. Algebra, 515 (2018), 278–297.

[M11] Mattarei, S., Engel conditions and symmetric tensors, Linear Multilinear Algebra, 59 (4) (2011), 441–449.

[M06] Moreau, A., Indice du normalisateur du centralisateur d'un élément nilpotent dans une algèbre de Lie semi-simple, Bull. Soc. Math. France, 134 (1) (2006), 83–117.

[NOV04] Newman, M. F., O'Brien, E. A., and Vaughan-Lee, M. R., Groups and nilpotent Lie rings whose order is the sixth power of a prime, J. Algebra, 278 (1) (2004), 383–401.

[OV05] O'Brien, E. A. and Vaughan-Lee, M. R., The groups with order $p^7$ for odd prime $p$, J. Algebra, 292 (1) (2005), 243–258.

[P99] Previtali, A., Maps behaving like exponentials and maximal unipotent subgroups of groups of Lie type, Comm. Algebra, 27 (5) (1999), 2511–2519.

[P18] Purslow, T., The restricted Ermolaev algebra and $F_4$, Exp. Math., 27 (3) (2018), 272–276.

[R00] Rossmanith, R., Lie centre-by-metabelian group algebras in even characteristic. I, II, Israel J. Math., 115 (2000), 51–75, 77–99.

[RT00] Rylands, L. J. and Taylor, D. E., Constructions for octonion and exceptional Jordan algebras, Des. Codes Cryptogr., 21 (1-3) (2000), 191–203
(Special issue dedicated to Dr. Jaap Seidel on the occasion of his 80th birthday (Oisterwijk, 1999)).

[SS18] Sahai, M. and Sharan, B., On Lie nilpotent modular group algebras, Comm. Algebra, 46 (3) (2018), 1199–1206.

[S05] Schneider, C., A computer-based approach to the classification of nilpotent Lie algebras, Experiment. Math., 14 (2) (2005), 153–160.

[SU11] Schneider, C. and Usefi, H., The isomorphism problem for universal enveloping algebras of nilpotent Lie algebras, J. Algebra, 337 (2011), 126–140.

[SU16] Schneider, C. and Usefi, H., The classification of $p$-nilpotent restricted Lie algebras of dimension at most 4, Forum Math., 28 (4) (2016), 713–727.

[S95] Short, M. W., A conjecture about free Lie algebras, Comm. Algebra, 23 (8) (1995), 3051–3057.

[S06] Siciliano, S., Cartan subalgebras in Lie algebras of associative algebras, Comm. Algebra, 34 (12) (2006), 4513–4522.

[S07] Strade, H., Lie algebras of small dimension, in Lie algebras, vertex operator algebras and their applications, Amer. Math. Soc., Providence, RI, Contemp. Math., 442 (2007), 233–265.

[PR14] van Pruijssen, M. and Román, P., Matrix valued classical pairs related to compact Gelfand pairs of rank one, SIGMA Symmetry Integrability Geom. Methods Appl., 10 (2014), Paper 113, 28.

[W18] Whybrow, M. L., Majorana algebras generated by a $2A$ algebra and one further axis, J. Group Theory, 21 (3) (2018), 417–437.

[XJL15] Xie, W., Jin, Q., and Liu, W., $\rm Hom$-structures on semi-simple Lie algebras, Open Math., 13 (1) (2015), 617–630.

[XY14] Xu, Y. and Yang, S., PBW-deformations of quantum groups, J. Algebra, 408 (2014), 222–249.

[Z13] Zelikson, S., On crystal operators in Lusztig's parametrizations and string cone defining inequalities, Glasg. Math. J., 55 (1) (2013), 177–200.

[Z10] Zusmanovich, P., $\omega$-Lie algebras, J. Geom. Phys., 60 (6-8) (2010), 1028–1044.

[Z10] Zusmanovich, P., On $\delta$-derivations of Lie algebras and superalgebras, J. Algebra, 324 (12) (2010), 3470–3486.

[Z14] Zusmanovich, P., Erratum to ``On $\delta$-derivations of Lie algebras and superalgebras'' [J. Algebra 324 (12) (2010) 3470–3486] [MR2735394], J. Algebra, 410 (2014), 545–546.

[Z17] Zusmanovich, P., Special and exceptional mock-Lie algebras, Linear Algebra Appl., 518 (2017), 79–96.