Ideals in Graph Algebras

2012/05/06 by Ruiz, Efren, Tomforde, Mark · 1 citation
#16D25 #46L55 #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1205.1247

Abstract

We show that the graph construction used to prove that a gauge-invariant ideal of a graph C*-algebra is isomorphic to a graph C*-algebra, and also used to prove that a graded ideal of a Leavitt path algebra is isomorphic to a Leavitt path algebra, is incorrect as stated in the literature. We give a new graph construction to remedy this problem, and prove that it can be used to realize a gauge-invariant ideal (respectively, a graded ideal) as a graph C*-algebra (respectively, a Leavitt path algebra).

Cited by

• Z-stable Graph Algebras

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