TY - JOUR
T1 - Module theory over Leavitt path algebras and K-theory
AU - Ara, Pere
AU - Brustenga, Miquel
PY - 2010/7/1
Y1 - 2010/7/1
N2 - 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 Lk (E) and show its close relationship with the finite-dimensional representations of the inverse quiver over(E, -) of E, as well as with the class of finitely generated Pk (E)-modules M such that TorqPk (E) (k| E0 |, M) = 0 for all q, where Pk (E) is the usual path algebra of E. By using these results we compute the higher K-theory of the von Neumann regular algebra Qk (E) = Lk (E) Σ- 1, where Σ is the set of all square matrices over Pk (E) which are sent to invertible matrices by the augmentation map ε{lunate} : Pk (E) → k| E0 |. © 2009 Elsevier B.V. All rights reserved.
AB - 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 Lk (E) and show its close relationship with the finite-dimensional representations of the inverse quiver over(E, -) of E, as well as with the class of finitely generated Pk (E)-modules M such that TorqPk (E) (k| E0 |, M) = 0 for all q, where Pk (E) is the usual path algebra of E. By using these results we compute the higher K-theory of the von Neumann regular algebra Qk (E) = Lk (E) Σ- 1, where Σ is the set of all square matrices over Pk (E) which are sent to invertible matrices by the augmentation map ε{lunate} : Pk (E) → k| E0 |. © 2009 Elsevier B.V. All rights reserved.
U2 - https://doi.org/10.1016/j.jpaa.2009.10.001
DO - https://doi.org/10.1016/j.jpaa.2009.10.001
M3 - Article
VL - 214
SP - 1131
EP - 1151
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
ER -