Project Details
Projekt
Standard basis methods for path algebra quotients
Applicant
Dr. Simon Alexander King
Subject Area
Mathematics
Term
from 2013 to 2016
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 239464324
The projected implementation of the non-commutative F5 algorithm, e.g., in the Letterplace algebra, is of general interest. An extension of the theory to infinite dimensional path algebra quotients would conceivably be applicable to the computation of Loewy layers. In homological algebra, an efficient non-commutative F5 implementation can be used to extend existing packages for the computation of modular group cohomology. Cohomology computations shall thus become possible in previously untractable examples, as well as testing conjectures on modular cohomology. I plan to study Ian Hambleton's conjecture that the modular cohomology of finite groups is detected on metabelian p-groups. In connection with isomorphism tests for graded algebras, I intend to investigate Bettina Eick's conjecture on cohomology and coclass of p-groups.I will also compute Ext-algebras of groups and basic algebras. Non-commutative standard bases not only play a role in the computation of resolutions, but also in the computation of the ring structure. Such computations require a large background of software packages, ranging from linear algebra over GAP and Singular to new software. The new software shall be published as part of the Sage standard library. Data bases shall be created for Sage and Gap. In addition, I'll try to extend known degree bounds of cohomology rings to Ext-algebras.
DFG Programme
Priority Programmes
