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arXiv · 1705.08024

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

Gwyn Bellamy·Ulrich Thiel
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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.

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BibTeXRIS

Gwyn Bellamy, Ulrich Thiel. 2017-05-22. Highest weight theory for finite-dimensional graded algebras with triangular decomposition. https://doi.org/10.1016/j.aim.2018.03.011

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