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On the Hochschild cohomology of finite group algebras

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GRA2 - Groups, representations and applications: new perspectives

Some of the long standing conjectures in modular representation theory suggest that a very small amount of information on a block of a finite group algebra, such as the dimension of its center, determines a considerable amount of structural information of that block algebra, if not outright, then up to finitely many possibilities. Noting that the center is the degree zero Hochschild cohomology, we describe some of the known as well as conjecturally expected connections between the Hochschild cohomology of a block and its algebra structure, with an emphasis on the Lie algebra structure of the first Hochschild cohomology space.

This talk is part of the Isaac Newton Institute Seminar Series series.

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