Highest weight theory for finite-dimensional graded algebras with triangular decomposition

Bellamy, G. and Thiel, U. (2018) Highest weight theory for finite-dimensional graded algebras with triangular decomposition. Advances in Mathematics, 330, pp. 361-419. (doi:10.1016/j.aim.2018.03.011)

Bellamy, G. and Thiel, U. (2018) Highest weight theory for finite-dimensional graded algebras with triangular decomposition. Advances in Mathematics, 330, pp. 361-419. (doi:10.1016/j.aim.2018.03.011)

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Abstract

We show that the category of graded modules over a finite-dimensional graded algebra admitting a triangular decomposition can be endowed with the structure of a highest weight category. When the algebra is self-injective, we show furthermore that this highest weight category has tilting modules in the sense of Ringel. This provides a new perspective on the representation theory of such algebras, and leads to several new structures attached to them. There are a wide variety of examples in algebraic Lie theory to which this applies: restricted enveloping algebras, Lusztig's small quantum groups, hyperalgebras, finite quantum groups, and restricted rational Cherednik algebras.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Bellamy, Dr Gwyn
Authors: Bellamy, G., and Thiel, U.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Advances in Mathematics
Publisher:Elsevier
ISSN:0001-8708
ISSN (Online):1090-2082
Published Online:30 March 2018
Copyright Holders:Copyright © 2018 Elsevier Inc.
First Published:First published in Advances in Mathematics 330:361-419
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
662571Symplectic representation theoryGwyn BellamyEngineering and Physical Sciences Research Council (EPSRC)EP/N005058/1M&S - MATHEMATICS