Computing decompositions of modules over finite-dimensional algebras. (English) Zbl 1131.16024

Lux, Klaus M.; Szőke, Magdolna

Exp. Math. 16, No. 1, 1-6 (2007).

Summary: Based on our method for determining endomorphism rings [K. M. Lux, M. Szőke, Exp. Math. 12, No. 1, 91-98 (2003; Zbl 1048.16029)], we describe an algorithm to compute decompositions of modules of finite-dimensional algebras over finite fields. The algorithm is implemented in the C-Meat-Axe [M. Ringe, The C-Meat-Axe. (http://www.math.rwth-aachen.de/homes/MTX/), 1994].

MSC:

16Z05	Computational aspects of associative rings (general theory)
16P10	Finite rings and finite-dimensional associative algebras
16S50	Endomorphism rings; matrix rings
16-04	Software, source code, etc. for problems pertaining to associative rings and algebras
20C40	Computational methods (representations of groups) (MSC2010)
16D70	Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
68W30	Symbolic computation and algebraic computation

Keywords:

endomorphism rings; decompositions of modules; algorithms; modular representation theory

Citations:

Zbl 1048.16029

Software:

MeatAxe