Module theory over Leavitt path algebras and $K$-theory
| dc.creator | Ara, Pere | |
| dc.creator | Brustenga, Miquel | |
| dc.date | 2009-05-23 | |
| dc.date.accessioned | 2026-07-07T13:17:48Z | |
| dc.date.available | 2026-07-07T13:17:48Z | |
| dc.description | Let $k$ be a field and let $E$ be a finite quiver. We study the structure of the finitely presented modules of finite length over the Leavitt path algebra $L_k (E)$ and show its close relationship with the finite-dimensional representations of the inverse quiver $\overline{E}$ of $E$, as well as with the class of finitely generated $P_k(E)$-modules $M$ such that ${\rm Tor}_q^{P_k (E)}(k^{|E^0|},M)=0$ for all $q$, where $P_k(E)$ is the usual path algebra of $E$. By using these results we compute the higher $K$-theory of the von Neumann regular algebra $Q_k (E)=L_k (E)Σ^{-1}$, where $Σ$ is the set of all square matrices over $P_k (E)$ which are sent to invertible matrices by the augmentation map $ε\colon P_k (E)\to k^{|E^0|}$. | |
| dc.description | 31 pages | |
| dc.identifier | https://arxiv.org/abs/0905.3827 | |
| dc.identifier | http://arxiv.org/abs/0905.3827 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/231233 | |
| dc.subject | Rings and Algebras | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 16D70; 16D90 | |
| dc.title | Module theory over Leavitt path algebras and $K$-theory | |
| dc.type | text |