论文标题
$ q = 0 $：type $ a_ {n} $案例的量化函数代数
Quantized function algebras at $q=0$: type $A_{n}$ case
论文作者
论文摘要
我们将量化函数代数的概念定义为$ q = 0 $或类型$ a_ {n} $ compact lie lie组的$ q $变形在$ c^*$ - 代数级别。 $ c^{*} $ - algebra $ a_ {n}（0）$定义为一个有限的生成器和关系集给出的通用$ c^*$ - 代数。我们通过查看$ q> 0 $的量化函数代数的不可约表示，并在适当地重新恢复生成元件后，以$ q \ to $ q \ 0+$来获得这些关系。然后，我们证明，在$ n = 2 $案例中，$ a_ {2}（0）$不可约为$ q \ to $ q \ to 0+$ limits的$ c^*$ - 代数 - 代数 - emgebras $ a_ {2}（q）$。
We define the notion of quantized function algebras at $q=0$ or crystallization of the $q$ deformations of the type $A_{n}$ compact Lie groups at the $C^*$-algebra level. The $C^{*}$-algebra $A_{n}(0)$ is defined as a universal $C^*$-algebra given by a finite set of generators and relations. We obtain these relations by looking at the irreducible representations of the quantized function algebras for $q>0$ and taking limit as $q\to 0+$ after rescaling the generating elements appropriately. We then prove that in the $n=2$ case the irreducible representations $A_{2}(0)$ are precisely the $q\to 0+$ limits of the irreducible representations of the $C^*$-algebras $A_{2}(q)$.
