Inductive Limits of Toeplitz Algebras |
Received:June 28, 2004 |
Key Words:
Toeplitz algebra inductive limit.
|
Fund Project: |
|
Hits: 3052 |
Download times: 1399 |
Abstract: |
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. |
Citation: |
DOI:10.3770/j.issn:1000-341X.2006.03.021 |
View Full Text View/Add Comment |
|
|
|