{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T03:00:15Z","timestamp":1770519615834,"version":"3.49.0"},"reference-count":27,"publisher":"World Scientific Pub Co Pte Ltd","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Algebra Appl."],"published-print":{"date-parts":[[2022,10]]},"abstract":"<jats:p> 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 [Formula: see text] and two polynomials [Formula: see text]. 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.\u00a034(15) (2001) 3253; R. L\u00fc and K. Zhao, Finite-dimensional simple modules over generalized Heisenberg algebras, Linear Algebra Appl.\u00a0475 (2015) 276\u2013291, MR 3325233]) as well as generalized down-up algebras (as defined in [G. Benkart and T. Roby, Down-up algebras, J. Algebra\u00a0209(1) (1998) 305\u2013344; T. Cassidy and B. Shelton, Basic properties of generalized down-up algebras, J. Algebra\u00a0279(1) (2004) 402\u2013421, 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. <\/jats:p>","DOI":"10.1142\/s0219498822502048","type":"journal-article","created":{"date-parts":[[2021,6,5]],"date-time":"2021-06-05T03:13:31Z","timestamp":1622862811000},"source":"Crossref","is-referenced-by-count":3,"title":["Structure and isomorphisms of quantum generalized Heisenberg algebras"],"prefix":"10.1142","volume":"21","author":[{"given":"Samuel A.","family":"Lopes","sequence":"first","affiliation":[{"name":"CMUP, Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade do Porto, Rua do Campo Alegre s\/n, 4169\u2013007 Porto, Portugal"}]},{"given":"Farrokh","family":"Razavinia","sequence":"additional","affiliation":[{"name":"CMUP, Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade do Porto, Rua do Campo Alegre s\/n, 4169\u2013007 Porto, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2021,7,6]]},"reference":[{"key":"S0219498822502048BIB001","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/aaad6d"},{"key":"S0219498822502048BIB002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-00-02678-7"},{"key":"S0219498822502048BIB003","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1998.7511"},{"key":"S0219498822502048BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2010.11.027"},{"key":"S0219498822502048BIB005","doi-asserted-by":"publisher","DOI":"10.1080\/00927870802209987"},{"key":"S0219498822502048BIB006","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1999.8263"},{"key":"S0219498822502048BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2004.05.009"},{"key":"S0219498822502048BIB008","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/34\/15\/304"},{"key":"S0219498822502048BIB009","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.87.052120"},{"key":"S0219498822502048BIB010","doi-asserted-by":"publisher","DOI":"10.1080\/00927877908822438"},{"key":"S0219498822502048BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0346-0286-0_12"},{"key":"S0219498822502048BIB012","series-title":"London Mathematical Society Student Texts","volume-title":"An Introduction to Noncommutative Noetherian Rings","volume":"16","author":"Goodearl K. 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