Dear Gap forum,
Has anyone implemented tensor products for modules?
The C-MeatAxe of Lehrstuhl D at Aachen has routines for dealing with
tensor products of matrices (Kronecker product). Is this what you mean
by "tensor products for modules".
Anyone have methods for
finitely generated projective modules in general, and ones over integral
rings in particular? Rings of algebraic integers? These questions are
related to representations of "quantum groups".
People working in computational algebraic number theory must have experience
with finitely generated modules over rings of algebraic integers. Here is the
web address of KANT, a system for doing algebraic number theory:
There are suggestions of Richard Parker for "An Integral Meat-Axe" in:
Curtis and Wilson (Eds.), The Atlas of Finite Groups: Ten Years On,
London Math. Soc. Lecture Note Series 249, Cambridge University Press,
1998. This would work for modules over the rational integers trying to
find, for example, non-trivial (pure) submodules.So far I am not aware of any
implementation of such an integral meat-axe.
Lintons vector enumerator is a method to construct modules for finitely
presented algebras (and might be of interest for constructing repersentations
of quantum groups). Implementations of the vector enumerator only exist for
finite ground fields, but there is a student at Lehrstuhl D who is currently
implementing a more genral version of the vector enumerator which should
work, in principle, over polynomial rings or function fields.