Abstract
The generalized quantum Euclidean group \({{\cal O}_q}({\mathfrak{b}_{m,n}})\) is a natural generalization of the quantum Euclidean group \({{\cal O}_q}({\mathfrak{b}_{1,1}})\). The Heisenberg double \({{\cal D}_q}({\mathfrak{b}_{m,n}})\) of \({{\cal O}_q}({\mathfrak{b}_{m,n}})\) is the smash product of \({{\cal O}_q}({\mathfrak{b}_{m,n}})\) with its Hopf dual \({{\cal U}_q}({\mathfrak{b}_{m,n}})\). In this paper, we study the weight modules, the prime spectrum and the automorphism group of the Heisenberg double \({{\cal D}_q}({\mathfrak{b}_{m,n}})\).
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The author gratefully acknowledges partial financial supports from the National Natural Science Foundation of China (Nos. 11871249, 12171155).
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Xia, L. Heisenberg Double of the Generalized Quantum Euclidean Group and Its Representations. Front. Math (2024). https://doi.org/10.1007/s11464-022-0332-7
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DOI: https://doi.org/10.1007/s11464-022-0332-7