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On the Hochschild cohomology of blocks of finite group algebras

Murphy, W. (2023). On the Hochschild cohomology of blocks of finite group algebras. (Unpublished Diploma thesis, City, University of London)


This thesis sets out to investigate the first Hochschild cohomology of finite group algebras and their blocks, as well as of twisted group algebras. We employ a range of methods and techniques to calculate the structure of some explicit examples, as well as develop the general theory. Our first main result, found in Chapter 3, is actually an alternative proof of our own pre-existing result that a certain 9-dimensional algebra does not arise as the basic algebra of a block; this time round we use Hochschild cohomology as a key ingredient. Our second main result, in Chapter 4, concerns the Lie algebra structure of the first Hochschild cohomology of the Mathieu groups, and in particular we show that these Lie algebras are nontrivial for blocks with a nontrivial defect group. Our third and final main result in Chapter 5 concerns the first Hochschild cohomology of twisted group algebras, and we show that their Lie algebras are also nontrivial for the twisted group algebras of the finite simple groups

Publication Type: Thesis (Diploma)
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
School of Science & Technology > School of Science & Technology Doctoral Theses
Doctoral Theses
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