论文标题
量子广义的海森堡代数的结构和同构
Structure and isomorphisms of quantum generalized Heisenberg algebras
论文作者
论文摘要
在[14]中，我们介绍了一个新的代数类，我们将其命名为\ textit {Quantum Permerized Heisenberg代数}，并依赖于参数$ Q $和两个多项式$ 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 $q\neq 1$ and $\, \mathsf{deg}\, f>1$).在[14]中对其有限维的不可约合表示分类后，在本文中，我们通过同构，对其自动形态群体的描述以及对Gelfand-Kirillov Dimension等环理论特性的研究和研究。
In [14] we introduced a new class of algebras, which we named \textit{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 $q\neq 1$ and $\, \mathsf{deg}\, f>1$). 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.
