Universität
Paderborn, FB
17 Mathematik, AG
von zur Gathen
Project:
Algorithms for Finite Dimensional Algebras and Modules
There should be a library of algorithms allowing to deal nicely with finite
dimensional algebras and modules. For example, someone tells you an algebra
as a subalgebra of a matrix algebra or as a multiplication tensor, or a
modular group algebra. Compute a description of this algebra as a quotient
of a quiver algebra. What about deciding whether two algebras are isomorphic?
Or compute a MORITA-Transform. Compute the AUSLANDER-REITEN-quiver.
Or ...
Let's be modest. Construct a system to define an algebra and modules
over an algebra. [Compare e.g. MAGMA.] Provide routines to convert one
representation to another. Things like direct sum of modules, direct sum
(product) and tensor product of algebras should be no problem. ...
If possible use combinatorial algorithms. But also algebraic tools should
be available and applicable, e.g. GRÖBNER-basis
algorithms (in a polynomial algebra k[X1,...,Xn]
or in a quiver algebra kQ or ...).
Literature
CREP
OPAL
Michael Nüsken,