论文标题
$ su_ {q}（2）$的GNS表示的GNS表示形式的近似等效性
An approximate equivalence for the GNS representation of the Haar state of $SU_{q}(2)$
论文作者
论文摘要
我们使用结晶的$ c^*$ - 代数$ c（su_ {q}（2））$ at $ q = 0 $，获得一个单一的统一性，以涉及$ l^{2} $ gns代表的近似值$ c^{*} $ - algebra $ c（su_ {q}（2））$对于参数$ q $的非零值。这种近似等效性从cuntz图片中给出了$ kk $类，从quasihomormormormisms以及双量子组的弗雷德尔姆表示，$ c^*$ - 代理在mishchenko的意义上，具有系数的双量子组$ \ widehat {su_q（2）} $。
We use the crystallised $C^*$-algebra $C(SU_{q}(2))$ at $q=0$ to obtain a unitary that gives an approximate equivalence involving the GNS representation on the $L^{2}$ space of the Haar state of the quantum $SU(2)$ group and the direct integral of all the infinite dimensional irreducible representations of the $C^{*}$-algebra $C(SU_{q}(2))$ for nonzero values of the parameter $q$. This approximate equivalence gives a $KK$ class via the Cuntz picture in terms of quasihomomorphisms as well as a Fredholm representation of the dual quantum group $\widehat{SU_q(2)}$ with coefficients in a $C^*$-algebra in the sense of Mishchenko.
