### Abstract

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 | |

Publication status | Published - Dec 2017 |

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### Cite this

*Journal of Pure and Applied Algebra*,

*221*(12), 2953-2973. https://doi.org/10.1016/j.jpaa.2017.02.010

**On blocks of defect two and one simple module, and Lie algebra structure of HHⁱ.** / Benson, David; Kessar, Radha; Linckelmann, Markus.

Research output: Contribution to journal › Article

*Journal of Pure and Applied Algebra*, vol. 221, no. 12, pp. 2953-2973. https://doi.org/10.1016/j.jpaa.2017.02.010

}

TY - JOUR

T1 - On blocks of defect two and one simple module, and Lie algebra structure of HHⁱ

AU - Benson, David

AU - Kessar, Radha

AU - Linckelmann, Markus

N1 - The first author thanks City, University of London for its hospitality during the preparation of this paper.

PY - 2017/12

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.

U2 - 10.1016/j.jpaa.2017.02.010

DO - 10.1016/j.jpaa.2017.02.010

M3 - Article

VL - 221

SP - 2953

EP - 2973

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 12

ER -