Corners of graph algebras

Abstract

It is known that given a directed graph E and a subset X of vertices, the sum of the projections associated to the vertices in X in the C*-algebra of E converges strictly in the multiplier algebra to a projection P. Here we give a construction which, in certain cases, produces a directed graph F whose C*-algebra is isomorphic to the corner P(C*(E))P. Corners of this type arise naturally as the fixed point algebras of discrete coactions on graph algebras related to labellings. We prove this fact, and show that our construction is applicable to such a case whenever the labelling satisfies an analogue of Kirchhoff's voltage law.

16 pages; uses XY-Pic

References in corpus (2)

• Computing K-theory and Ext for graph C*-algebras
• Skew products and crossed products by coactions

Cited by in corpus (6)

• Refined moves for structure-preserving isomorphism of graph C*-algebras
• Notes on quantum weighted projective spaces and multidimensional teardrops
• Simplicity of the C*-algebras of skew product k-graphs
• Fredholm modules over graph C*-algebras
• Gauge Invariant Uniqueness Theorem for Corners of k-graphs
• Subsets of vertices give Morita equivalences of Leavitt path algebras