AsUnitalSubalgebra( A, U )
Let A be a parent algebra and U be a parent algebra or a subalgebra
with a possibly different parent algebra, such that the generators of U
are elements of A.
AsSubalgebra returns a new unital subalgebra S
such that S has parent algebra A and is generated by the generators
of U. If U or A do not contain the zero-th power of elements an
error is signalled.
gap> a:= [ [ 1, 0 ], [ 0, 0 ] ];; gap> b:= [ [ 0, 0 ], [ 0, 1 ] ];; gap> alg:= Algebra( Rationals, [ a, b ] );; gap> alg.name:= "alg";; gap> s:= UnitalAlgebra( Rationals, [ a ] ); UnitalAlgebra( Rationals, [ [ [ 1, 0 ], [ 0, 0 ] ] ] ) gap> AsSubalgebra( alg, s ); Subalgebra( alg, [ [ [ 1, 0 ], [ 0, 0 ] ], [ [ 1, 0 ], [ 0, 1 ] ] ] ) gap> AsUnitalSubalgebra( alg, s ); UnitalSubalgebra( alg, [ [ [ 1, 0 ], [ 0, 0 ] ] ] )Note that
AsUnitalSubalgebraare the only functions in which the name
Subalgebradoes not refer to the mathematical terms subalgebra and superalgebra but to the implementation of algebras as subalgebras and parent algebras.
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