Regular Nilpotent Elements and Quantum Groups

Regular maps with nilpotent automorphism groups

According to a folklore result, every regular map on an orientable surface with abelian automorphism group belongs to one of three infinite families of maps with one or two vertices. Here we deal with regular maps whose automorphism group is nilpotent. We show that each such map decomposes into a direct product of two maps H×K, where Aut(H) is a 2-group and K is a map with a single vertex and a...

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup

Regular Elements of Finite Reflection Groups

On Cocharacters Associated to Nilpotent Elements of Reductive Groups

Let G be a connected reductive linear algebraic group defined over an algebraically closed field of characteristic p. Assume that p is good for G. In this note we consider particular classes of connected reductive subgroups H of G and show that the cocharacters of H that are associated to a given nilpotent element e in the Lie algebra of H are precisely the cocharacters of G associated to e tha...

Auslander-regular and Cohen-macaulay Quantum Groups

Let Uq(C) be the quantum group or quantized enveloping algebra in the sense of [6, 7] associated to a Cartan matrix C. A relevant property of Uq(C) is that it can be endowed with a multi-filtration such that the associated multi-graded algebra is an easy localization of the coordinate ring of a quantum affine space [7, Proposition 10.1]. Thus, it is not surprising if we claim that Uq(C) is an A...