Homological algebra and group algebras
Jon F. Carlson
Athens, GA
This lecture is a survey of some continuing projects to
develop computational capabilities for homological algebra
over group algebras and other rings. Applications have
included the computation of group cohomology and the geometry
of cohomology rings, computations of support varieties of
modules and the structure and cohomology of Hecke algebras.
Some emphasis in the lecture will be given to the newly
implemented algorithms for calculating generators and
relations for matrix algebras defined over finite fields.