$q$ -分次Heisenberg代数与变形超对称
$q$-graded Heisenberg algebras and deformed supersymmetries
摘要：
对单位圆盘上的$q$复数，在q-变形Heisenberg代数的乘积生成的包络代数上引入了$q$-分次的概念.在这个公式中，我们考虑了包络代数中超对称概念的扩展。我们恢复普通的$\mathbb{Z}_2$分级或格拉斯曼奇偶结合超代数，和通常的超对称性的修改版本。作为一个具体的问题，我们专注于有趣的限制$q\to -1$的阿里克和库恩变形的海森堡代数允许映射到玻色子的费米子模式在修改的意义上。不同的代数后果进行了讨论。
英文摘要：
The notion of $q$-grading on the enveloping algebra generated by products of q-deformed Heisenberg algebras is introduced for $q$ complex number in the unit disc. Within this formulation, we consider the extension of the notion of supersymmetry in the enveloping algebra. We recover the ordinary $\mathbb{Z}_2$ grading or Grassmann parity for associative superalgebra, and a modified version of the usual supersymmetry. As a specific problem, we focus on the interesting limit $q\to -1$ for which the Arik and Coon deformation of the Heisenberg algebra allows to map fermionic modes to bosonic ones in a modified sense. Different algebraic consequences are discussed.
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