Computing homomorphism spaces between modules over finite dimensional algebras. (English) Zbl 1048.16029

Lux, Klaus M.; Szőke, Magdolna

Exp. Math. 12, No. 1, 91-98 (2003).

Summary: We describe an algorithm to compute homomorphism spaces between modules of finite dimensional algebras over finite fields. The algorithm is implemented in the C-Meat-Axe.

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)

Keywords:

homomorphism spaces; algorithms; finite-dimensional algebras; endomorphism rings

Software:

MeatAxe; Magma

References:

[1]	Bosma W., Handbook of Magma Functions (1999)
[2]	DOI: 10.1006/jsco.2001.0454 · Zbl 1045.16007 · doi:10.1006/jsco.2001.0454
[3]	DOI: 10.1006/jsco.1994.1033 · Zbl 0828.16001 · doi:10.1006/jsco.1994.1033
[4]	Lux K. M., Decomposing Modules of Finite Dimensional Algebras (2003)
[5]	DOI: 10.1006/jsco.1999.1009 · Zbl 0983.20010 · doi:10.1006/jsco.1999.1009
[6]	Parker, R. A. 1984.The Computer Calculation of Modular Characters (the Meat-Axe).Edited by: Atkinson, M. D. 267–274. New York: Academic Press. [Parker 84], InComputational Group Theory, edited by · Zbl 0555.20001
[7]	Ringe M., The C-Meat-Axe, Version 2.4.0. (2001)
[8]	DOI: 10.1016/S0747-7171(08)80078-8 · Zbl 0703.20009 · doi:10.1016/S0747-7171(08)80078-8
[9]	Szöke M., Computing Green Correspondents of Weight Modules. (1998) · Zbl 0980.20006