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Algebra and Geometry Seminar

Monday, April 30, 2018
4:00pm to 5:00pm
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Building 15, Room 104
Finite-dimensio​nal graded algebras with triangular decomposition
Ulrich Thiel, School of Mathematics and Statistics, University of Sydney,

I will discuss a new approach to the representation theory of self-injective finite-dimensio​nal graded algebras with triangular decomposition (such as restricted enveloping algebras, Lusztig's small quantum groups, hyperalgebras, finite quantum groups, restricted rational Cherednik algebras, etc). We show that the graded module category of such an algebra is a highest weight category and has a tilting theory in the sense of Ringel. We can then show that the degree zero part of the algebra (the "core") is cellular and can construct a canonical highest weight cover à la Rouquier of it. The core captures essential information of the representation theory of the original algebra, hence we can approach the latter with these additional structures. This is joint work with Gwyn Bellamy (Glasgow).

For more information, please contact Mathematics Dept. by phone at 626-395-4335 or by email at [email protected].