Regularity conditions for arbitrary Leavitt path algebras

Autor:	Abrams, G., Rangaswamy, K. M.
Rok vydání:	2008
Předmět:	Mathematics - Rings and Algebras Mathematics - Operator Algebras 16S99 16E50
Druh dokumentu:	Working Paper
Popis:	We show that if $E$ is an arbitrary acyclic graph then the Leavitt path algebra $L_K(E)$ is locally $K$-matricial; that is, $L_K(E)$ is the direct union of subalgebras, each isomorphic to a finite direct sum of finite matrix rings over the field $K$. As a consequence we get our main result, in which we show that the following conditions are equivalent for an arbitrary graph $E$: (1) $L_K(E)$ is von Neumann regular. (2) $L_K(E)$ is $\pi$-regular. (3) $E$ is acyclic. (4) $L_K(E)$ is locally $K$-matricial. (5) $L_K(E)$ is strongly $\pi$-regular. We conclude by showing how additional regularity conditions (unit regularity, strongly clean) can be appended to this list of equivalent conditions. Comment: 15 pages, accepted version July 2008 to appear Algebras and Representation Theory
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0806.3743 Zobrazit plný text záznamu View this record from Arxiv