Regularity conditions for arbitrary Leavitt path algebras
| dc.creator | Abrams, G. | |
| dc.creator | Rangaswamy, K. M. | |
| dc.date | 2008-06-23 | |
| dc.date | 2008-10-05 | |
| dc.date.accessioned | 2026-07-07T10:07:16Z | |
| dc.date.available | 2026-07-07T10:07:16Z | |
| dc.description | 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 $π$-regular. (3) $E$ is acyclic. (4) $L_K(E)$ is locally $K$-matricial. (5) $L_K(E)$ is strongly $π$-regular. We conclude by showing how additional regularity conditions (unit regularity, strongly clean) can be appended to this list of equivalent conditions. | |
| dc.description | 15 pages, accepted version July 2008 to appear Algebras and Representation Theory | |
| dc.identifier | https://arxiv.org/abs/0806.3743 | |
| dc.identifier | http://arxiv.org/abs/0806.3743 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170573 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Operator Algebras | |
| dc.subject | 16S99; 16E50 | |
| dc.title | Regularity conditions for arbitrary Leavitt path algebras | |
| dc.type | text |