Heisenberg double of some quantum group and its representations
Abstract
Let $\mathfrak{g},\mathfrak{h}$ be two indecomposable solvable Lie algebras with dimension $5$ and special given structure constants. Their quantized universal enveloping algebras are Hopf algebras, and they are the Hopf duals of each other. The Heisenberg double $\mathcal{D}_{q}$ is the smash product of these two Hopf algebras. In this paper, we study the weight modules, the prime spectrum and the automorphism group of the Heisenberg double $\mathcal{D}_{q}$.
Fields of Study & Subjects
Advanced Topics in Algebra
Algebraic structures and combinatorial models
Advanced Operator Algebra Research
Publication details
- Journal / source
- Publicationes Mathematicae Debrecen
- Volume
- 108
- Issue
- 1-2
- Pages
- 201–209
- Publication date
- 1 January 2026