$C^*$-algebras of directed graphs and group actions
1999 ◽
Vol 19
(6)
◽
pp. 1503-1519
◽
Keyword(s):
Given a free action of a group $G$ on a directed graph $E$ we show that the crossed product of $C^* (E)$, the universal $C^*$-algebra of $E$, by the induced action is strongly Morita equivalent to $C^* (E/G)$. Since every connected graph $E$ may be expressed as the quotient of a tree $T$ by an action of a free group $G$ we may use our results to show that $C^* (E)$ is strongly Morita equivalent to the crossed product $C_0 ( \partial T ) \times G$, where $\partial T$ is a certain zero-dimensional space canonically associated to the tree.
Keyword(s):
2014 ◽
Vol 25
(07)
◽
pp. 1450065
◽
Keyword(s):
1993 ◽
Vol 04
(02)
◽
pp. 289-317
◽
Keyword(s):
Keyword(s):
2014 ◽
Vol 25
(02)
◽
pp. 1450010
◽
Keyword(s):
2016 ◽
Vol 59
(1)
◽
pp. 1-10
◽
Keyword(s):