Benson, D. J., Kessar, R. & Linckelmann, M. (2017).
On blocks of defect two and one simple module, and Lie algebra structure of HH¹.
*Journal of Pure and Applied Algebra*,
doi: /10.1016/j.jpaa.2017.02.010

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## Abstract

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.

Item Type: | Article |
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Additional Information: | © 2017, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ |

Uncontrolled Keywords: | math.RT; math.RT; math.GR; 20C20 |

Subjects: | Q Science > QA Mathematics |

Divisions: | School of Engineering & Mathematical Sciences > Department of Mathematical Science |

URI: | http://openaccess.city.ac.uk/id/eprint/14551 |

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