Standard basis methods for path algebra quotients/KI 861/2-1
A corner stone of the project is a non-commutative version of the F5 algorithm. It should provide an efficient way to compute standard bases in non-commutative settings, which has numerous applications. In contrast to other standard basis algorithms, the F5 algorithm additionally allows to compute Loewy layers of modules over basic algebras. In particular, it should provide a very efficient way to compute minimal projective resolutions for blocks of finite groups, which hopefully suffices to compute modular cohomology rings of groups that are currently out of reach (e.g., the mod-2 cohomology of Mathieu group M_24), and which can also be used for an incremental computation of Ext-algebras of blocks of finite groups. Standard bases are also used in isomorphism tests for f.p. graded commutative rings. This together with an improved computation of cohomology may be used to investigate conjectures of Eick--Leedham-Green on isomorphism types of cohomology rings and of Hambleton on essential classes.
DFG - Deutsche Forschungsgemeinschaft
|Laufzeit||November 2013 - Oktober 2015|
Dr. Simon A. King
Im Rahmen eines koordinierten Programms
|Bezeichnung des Koordinierten Programms||SPP 1489 "Algorithmic and Experimantal Methods in Algebra, Geometry and Number Theory"|