On blocks of defect two and one simple module, and Lie algebra structure of HHⁱ

David Benson, Radha Kessar, Markus Linckelmann

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Let k be a field of odd prime characteristic p. We calculate the Lie algebra structure of the first Hochschild cohomology of a class of quantum complete intersections over k. As a consequence, we prove that if B is a defect 2-block of a finite group algebra kG whose Brauer correspondent C has a unique isomorphism class of simple modules, then a basic algebra of B is a local algebra which can be generated by at most 2√ I elements, where I is the inertial index of B, and where we assume that k is a splitting field for B and C.
Original languageEnglish
Pages (from-to)2953-2973
Number of pages21
JournalJournal of Pure and Applied Algebra
Issue number12
Early online date24 Feb 2017
Publication statusPublished - Dec 2017


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