Hochschild cohomology of polynomial representations of GL2

Vanessa Miemietz; Will Turner

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

Hochschild cohomology of polynomial representations of GL₂

Vanessa Miemietz, Will Turner

Mathematical Science

University of East Anglia

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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
Pages (from-to)	117-170
Number of pages	54
Journal	Documenta Mathematica
Volume	23
DOIs	https://doi.org/10.25537/dm.2018v23.117-170
Publication status	Published - 1 Dec 2018

Bibliographical note

https://ojs.elibm.org/index.php/dm/about

The first author acknowledges support from ERC grant PERG07-GA-2010-268109. We would also like to thank the referee for an extremely thorough and helpful report.

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

Hochschild Cohomology of Polynomial Representations of GL2
© 2018 FIZ Karlsruhe GmbH. https://creativecommons.org/licenses/by/4.0/
Final published version, 408 KBLicence: CC BY

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

Cite this

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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.

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Hochschild cohomology of polynomial representations of GL2

Abstract

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William Turner

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Hochschild cohomology of polynomial representations of GL₂