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Structure and isomorphisms of quantum generalized Heisenberg algebras.
- Source :
-
Journal of Algebra & Its Applications . Oct2022, Vol. 21 Issue 10, p1-18. 18p. - Publication Year :
- 2022
-
Abstract
- In [S. A. Lopes and F. Razavinia, Quantum generalized Heisenberg algebras and their representations, preprint (2020), arXiv:2004.09301] we introduced a new class of algebras, which we named quantum generalized Heisenberg algebras and which depend on a parameter q and two polynomials f , g. We have shown that this class includes all generalized Heisenberg algebras (as defined in [E. M. F. Curado and M. A. Rego-Monteiro, Multi-parametric deformed Heisenberg algebras: A route to complexity, J. Phys. A: Math. Gen. 34(15) (2001) 3253; R. Lü and K. Zhao, Finite-dimensional simple modules over generalized Heisenberg algebras, Linear Algebra Appl. 475 (2015) 276–291, MR 3325233]) as well as generalized down-up algebras (as defined in [G. Benkart and T. Roby, Down-up algebras, J. Algebra 209(1) (1998) 305–344; T. Cassidy and B. Shelton, Basic properties of generalized down-up algebras, J. Algebra 279(1) (2004) 402–421, MR 2078408 (2005f:16051)]), but the parameters of freedom we allow for give rise to many algebras which are in neither one of these two classes. Having classified their finite-dimensional irreducible representations in [S. A. Lopes and F. Razavinia, Quantum generalized Heisenberg algebras and their representations, preprint (2020), arXiv:2004.09301], in this paper, we turn to their classification by isomorphism, the description of their automorphism groups and the study of their ring-theoretical properties. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LINEAR algebra
*ALGEBRA
*REPRESENTATIONS of algebras
*AUTOMORPHISM groups
Subjects
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 21
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 158906810
- Full Text :
- https://doi.org/10.1142/S0219498822502048