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

Algebra, Number Theory, Logic, and Representations (ANTLR)

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>2. 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 - 4 May 2018

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

HochschildCohomologyofGL2_2018Final published version, 408 KBLicence: CC BY

Vanessa Miemietz
- V.Miemietzuea.acuk
- School of Engineering, Mathematics and Physics - Professor in Pure Mathematics
- Algebra, Number Theory, Logic, and Representations (ANTLR) - Member
Person: Research Group Member, Academic, Teaching and Research

CAT REPTH: Categorification in Representation Theory.
Miemietz, V. (Principal Investigator)
CEC (Framework 7)
8/09/10 → 7/09/13
Project: Research

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>2. 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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Profiles

Vanessa Miemietz

Projects

CAT REPTH: Categorification in Representation Theory.

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Hochschild cohomology of polynomial representations of GL₂