### Abstract

Original language | English |
---|---|

Pages (from-to) | 389-411 |

Number of pages | 25 |

Journal | Journal of the London Mathematical Society |

Volume | 81 |

Issue number | 2 |

Early online date | 12 Feb 2010 |

DOIs | |

Publication status | Published - Apr 2010 |

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### Cite this

*Journal of the London Mathematical Society*,

*81*(2), 389-411. https://doi.org/10.1112/jlms/jdp078

**Hochschild and block cohomology varieties are isomorphic.** / Linckelmann, Markus.

Research output: Contribution to journal › Article

*Journal of the London Mathematical Society*, vol. 81, no. 2, pp. 389-411. https://doi.org/10.1112/jlms/jdp078

}

TY - JOUR

T1 - Hochschild and block cohomology varieties are isomorphic

AU - Linckelmann, Markus

PY - 2010/4

Y1 - 2010/4

N2 - We show that the varieties of the Hochschild cohomology of a block algebra and its block cohomology are isomorphic, implying positive answers to questions of Pakianathan and Witherspoon (‘Hochschild cohomology and Linckelmann cohomology for blocks of finite groups’, J. Pure Appl. Algebra 178 (2003) 87–100; ‘Quillen stratification for Hochschild cohomology of blocks’, Trans. Amer. Math. Soc. 358 (2005) 2897–2916). We obtain as a consequence that the cohomology H*(G; k) of a finite group G with coefficients in a field k of characteristic p is a quotient of the Hochschild cohomology of the principal block of kG by a nilpotent ideal.

AB - We show that the varieties of the Hochschild cohomology of a block algebra and its block cohomology are isomorphic, implying positive answers to questions of Pakianathan and Witherspoon (‘Hochschild cohomology and Linckelmann cohomology for blocks of finite groups’, J. Pure Appl. Algebra 178 (2003) 87–100; ‘Quillen stratification for Hochschild cohomology of blocks’, Trans. Amer. Math. Soc. 358 (2005) 2897–2916). We obtain as a consequence that the cohomology H*(G; k) of a finite group G with coefficients in a field k of characteristic p is a quotient of the Hochschild cohomology of the principal block of kG by a nilpotent ideal.

U2 - 10.1112/jlms/jdp078

DO - 10.1112/jlms/jdp078

M3 - Article

VL - 81

SP - 389

EP - 411

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 2

ER -