许庆祥,张小波.Toeplitz算子代数的归纳极限[J].数学研究及应用,2006,26(3):562~570
Toeplitz算子代数的归纳极限
Inductive Limits of Toeplitz Algebras
投稿时间:2004-06-28  
DOI:10.3770/j.issn:1000-341X.2006.03.021
中文关键词:  Toeplitz算子代数  归纳极限.
英文关键词:Toeplitz algebra  inductive limit.
基金项目:国家自然科学基金(10371051), 上海市自然科学基金(05ZR14094)和上海市教育委员会科研项目(05DZ04)
作者单位
许庆祥 上海师范大学数学系, 上海 200234 
张小波 上海师范大学数学系, 上海 200234 
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中文摘要:
      设$(G_1,E_1), (G_2,E_2)$为两个拟格序群,记${\cal T}^{E_1},{\cal T}^{E_2}$为相应的Toeplitz算子代数. 设$\phi: G_1\to G_2$为一个保单位的群同态, 使得$\phi(E_1)\subseteq E_2$. 本文给出了上述两个Toeplitz算子代数间的自然同态映照成为$C^*$-代数的单同态的充要条件,刻画了Toeplitz算子代数的归纳极限, 证明了任何自由群上的Toeplitz算子代数是顺从的.
英文摘要:
      Let $(G_1, E_1)$, $(G_2, E_2)$ be two quasi-lattice ordered groups, and ${\cal T}^{E_1}$, ${\cal T}^{E_2}$ be the associated Toeplitz algebras. Let $\phi: G_1\to G_2$ be a unital group homomorphism such that $\phi(E_1)\subseteq E_2$. This paper gives a necessary and sufficient condition under which the natural morphism from ${\cal T}^{E_1}$ to ${\cal T}^{E_2}$ becomes an injective $C^*$-algebra morphism. As an application, inductive limits of Toeplitz algebras are clarified. In particular, we show that Toeplitz algebras over free groups are always amenable.
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