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 |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Bellamy, Professor 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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