Hochschild cohomology of GL2

Vanessa Miemietz; William Brunt Turner

doi:10.25537/dm.2018v23.117-170

Hochschild cohomology of GL2

Vanessa Miemietz
, William Brunt Turner

Mathematical Science

University of East Anglia

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

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Abstract

We compute the Hochschild cohomology algebras of Ringel-self-dual blocks of polynomial representations of GL2 over an algebraically closed field of characteristic p>2, that is, of any block whose number of simple modules is a power of p. These algebras are finite-dimensional and we provide an explicit description of their bases and multiplications.

Original language	English
Number of pages	36
Journal	Documenta Mathematica
Volume	23
DOIs	https://doi.org/10.25537/dm.2018v23.117-170
Publication status	Published - 31 Dec 2018

Keywords

Hochschild cohomology
GL2
Koszul duality
differential graded algebras

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10.25537/dm.2018v23.117-170Licence: CC BY

Hochschild Cohomology of Polynomial Representations of
https://creativecommons.org/licenses/by/4.0/
Final published version, 408 KBLicence: CC BY

http://arxiv.org/abs/1107.2240Licence: Unspecified

William Turner
- School of Natural & Computing Sciences, Mathematical Science - Lecturer
Person: Academic

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AB - We compute the Hochschild cohomology algebras of Ringel-self-dual blocks of polynomial representations of GL2 over an algebraically closed field of characteristic p>2, that is, of any block whose number of simple modules is a power of p. These algebras are finite-dimensional and we provide an explicit description of their bases and multiplications.

KW - Hochschild cohomology

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KW - Koszul duality

KW - differential graded algebras

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M3 - Article

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VL - 23

JO - Documenta Mathematica

JF - Documenta Mathematica

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Hochschild cohomology of GL2

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William Turner

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