关于Hecke代数的包络C* 代数-代数
On enveloping C*-algebras of Hecke algebras
摘要：
给出了具有指定基的$^*$ -代数有包络$C^*$ -代数的一个充分条件.特别是Hecke代数$\h(G,\gm)$的情形，我们证明了在适当的假设下，不仅可以保证存在一个包络$C^*$ -代数$C^*(G, \gm)$，而且它与$L^1$ -Hecke代数的包络$C^*$ -代数$C^*(L^1(G,\gm))$重合.我们的方法被用来证明$C^*(G, \gm)$的存在性和与$C^*(L^1(G,\gm))$同构的几类Hecke代数。大多数已知满足这些属性的类都被这种方法所覆盖，我们还描述了一些新的。
英文摘要：
We give a sufficient condition for a $^*$-algebra with a specified basis to have an enveloping $C^*$-algebra. Particularizing to the setting of a Hecke algebra $\h(G,\gm)$, we show that under a suitable assumption not only we can assure that an enveloping $C^*$-algebra $C^*(G, \gm)$ exists, but also that it coincides with $C^*(L^1(G,\gm))$, the enveloping $C^*$-algebra of the $L^1$-Hecke algebra. Our methods are used to show the existence of $C^*(G, \gm)$ and isomorphism with $C^*(L^1(G,\gm))$ for several classes of Hecke algebras. Most of the classes which are known to satisfy these properties are covered by this approach, and we also describe some new ones.
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