2008/11/30 by Apoorva Khare
Mathematics · #math.RT #math.QA #msc:16D90 #msc:16S35
paper · pdf · doi:10.1080/00927870902829098
published as Communications in Algebra 37 (2009), no. 12, 4431-4475 · Final form of a much expanded, improved, and generalized version of a previous preprint - arXiv:math/0504371. Accepted for publication in Communications in Algebra; 45 pages, laTeX
arxiv created 2009/10/19 · arxiv updated 2015/02/02
This article aims to contribute to the study of algebras with triangular decomposition over a Hopf algebra, as well as the BGG Category O. We study functorial properties of O across various setups. The first setup is over a skew group ring, involving a finite group Γ acting on a regular triangular algebra A. We develop Clifford theory for A \rtimes Γ, and obtain results on block decomposition, complete reducibility, and enough projectives. O is shown to be a highest weight category when A satisfies one of the "Conditions (S)"; the BGG Reciprocity formula is slightly different because the duality functor need not preserve each simple module. Next, we turn to tensor products of such skew group rings; such a product is also a skew group ring. We are thus able to relate four different types of Categories O; more precisely, we list several conditions, each of which is equivalent in any one setup, to any other setup - and which yield information about O.