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Dear Frank,

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".

Best regards,

Frank Quinn

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:

http://www.math.tu-berlin.de/~kant/kash.html

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.

Best wishes,

Gerhard Hiss

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