Locally finite weighted Leavitt path algebras

2018/06/15 by Preusser, Raimund
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1806.06139

Abstract

A group graded K-algebra A=\bigoplus_{g∈ G} A_g is called "locally finite" if dim_K A_g < ∞ for every g∈ G. We characterise the weighted graphs (E,w) for which the weighted Leavitt path algebra L_K(E,w) is locally finite with respect to its standard grading. We also prove that the locally finite weighted Leavitt path algebras are precisely the Noetherian ones and that L_K(E,w) is locally finite iff (E,w) is finite and the Gelfand-Kirillov dimension of L_K(E,w) equals 0 or 1. Further it is shown that a locally finite weighted Leavitt path algebra is isomorphic to a locally finite Leavitt path algebra and therefore is isomorphic to a finite direct sum of matrix algebras over K and K[X,X^-1].

Related

• Weighted Leavitt path algebras of finite Gelfand-Kirillov dimension
• Weighted Leavitt path algebras that are isomorphic to unweighted Leavitt\n path algebras
• Leavitt path algebras of hypergraphs
• Leavitt path algebras of weighted and separated graphs
• The graded structure of Leavitt Path algebras