The Natural Morphisms between Toeplitz Algebras on Discrete Groups |
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| Authors: | Xu Qingxiang |
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| Institution: | Department of Mathematics, Shanghai Normal University Shanghai 200234, China, mathsci{at}shtu.edu.cn |
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| Abstract: | Let G be a discrete group and (G, G+) be a quasi-ordered group.Set  G+ (G+)–1 and G1= (G+\) {e}. Let FG1(G) andFG+(G) be the corresponding Toeplitz algebras. In the paper,a necessary and sufficient condition for a representation ofFG+(G) to be faithful is given. It is proved that when G isabelian, there exists a natural C*-algebra morphism from FG1(G)to FG+(G). As an application, it is shown that when G = Z2 andG+ = Z+ x Z, the K-groups K0(FG1(G))  Z2, K1(FG1(G)) Z andall Fredholm operators in FG1(G) are of index zero. |
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