2017/01/01 by Gwyn Bellamy, Bellamy, Gwyn, Ulrich Thiel +1 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.1705.08024
We show that the category of graded modules over a finite-dimensional graded\nalgebra admitting a triangular decomposition can be endowed with the structure\nof a highest weight category. When the algebra is self-injective, we show\nfurthermore that this highest weight category has tilting modules in the sense\nof Ringel. This provides a new perspective on the representation theory of such\nalgebras, and leads to several new structures attached to them. There are a\nwide variety of examples in algebraic Lie theory to which this applies:\nrestricted enveloping algebras, Lusztig's small quantum groups, hyperalgebras,\nfinite quantum groups, and restricted rational Cherednik algebras.\n