Computation of Gelfand–Kirillov dimension for B -type structures
Abstract
Let O(Spinq1/2(2n+1)) and O(SOq(2n+1)) denote the quantized algebras of regular functions on the Lie groups Spin(2n+1) and SO(2n+1), respectively. In this article, we prove that the Gelfand–Kirillov dimension of a simple unitarizable O(Spinq1/2(2n+1))-module Vt,wSpin is the same as the length of the associated Weyl word w. We further show that the same result holds for the O(SOq(2n+1))-module Vt,w, which is obtained from Vt,wSpin by restricting the algebra action to the subalgebra O(SOq(2n+1)) of O(Spinq1/2(2n+1)). Moreover, we consider the quantized algebras of regular functions on certain homogeneous spaces of SO(2n+1) and Spin(2n+1), and show that their Gelfand–Kirillov dimension coincides with the dimension of the corresponding homogeneous space as a real differentiable manifold.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Advanced Differential Geometry Research
Publication details
- Journal / source
- Communications in Algebra
- Publisher
- Informa UK Limited
- Volume
- 54
- Issue
- 10
- Pages
- 3314–3335
- Publication date
- 5 January 2026
- Language
- EN