2020/09/11 by Lopes, Samuel A., Razavinia, Farrokh
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2009.05270
In [14] 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 [8] and [16]) as well as generalized down-up algebras (as defined in [3] and [7]), but the parameters of freedom we allow give rise to many algebras which are in neither one of these two classes (if q≠ 1 and deg f>1). Having classified their finite-dimensional irreducible representations in [14], in this paper we turn to their classification by isomorphism, the description of their automorphism groups and the study of ring-theoretical properties like Gelfand-Kirillov dimension and being Noetherian.