Modular centralizer algebras.

摘要

We study centralizer algebras kGH for G a finite group with subgroup H. Our investigations are motivated by recent work due to H. Ellers and J. Murray. In particular, we study decompositions of these algebras, their self-injectivity, their representation type, and their cohomology. We specialize to the case of centralizer algebras corresponding to p-groups to obtain information on the Loewy structure of these centralizer algebras, generalizing Jennings' Theorem from modular representation theory. We also specialize to consider Hochschild cohomology of modular group algebras, building on recent work in this direction. Lastly, we analyze the symmetry of the endomorphism algebras for modules of the dihedral 2-groups. A number of concrete examples are given throughout to both illustrate and to build the theory, and many of these examples were suggested by computations performed using MAGMA.