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

David Benson; Radha Kessar; Markus Linckelmann

doi:10.1016/j.jpaa.2017.02.010

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

David Benson
, Radha Kessar
, Markus Linckelmann

Mathematical Science

City, University of London

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

15 Downloads (Pure)

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.

Original language	English
Pages (from-to)	2953-2973
Number of pages	21
Journal	Journal of Pure and Applied Algebra
Volume	221
Issue number	12
Early online date	24 Feb 2017
DOIs	https://doi.org/10.1016/j.jpaa.2017.02.010
Publication status	Published - Dec 2017

Bibliographical note

The first author thanks City, University of London for its hospitality during the preparation of this paper.

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© 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Accepted author manuscript, 336 KBLicence: CC BY-NC-ND

https://arxiv.org/abs/1604.04437Licence: Unspecified

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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.",

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AU - Kessar, Radha

AU - Linckelmann, Markus

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Y1 - 2017/12

N2 - 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.

AB - 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.

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DO - 10.1016/j.jpaa.2017.02.010

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JO - Journal of Pure and Applied Algebra

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ER -

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

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