### 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 |
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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

Benson, D., Kessar, R., & Linckelmann, M. (2017). On blocks of defect two and one simple module, and Lie algebra structure of HHⁱ.

*Journal of Pure and Applied Algebra*,*221*(12), 2953-2973. https://doi.org/10.1016/j.jpaa.2017.02.010