Leavitt vs. $C^{\ast }$ pullbacks

Abstract

We show that certain pullbacks of $\ast$-algebras equivariant with respect to a compact group action remain pullbacks upon completing to $C^{\ast }$-algebras. This unifies a number of results in the literature on graph algebras, showing that pullbacks of Leavitt path algebras lift automatically to pullbacks of the corresponding graph $C^{\ast }$-algebras.

7 pages + references; content changed substantially after feedback

References in corpus (2)

• Non-surjective pullbacks of graph C*-algebras from non-injective pushouts of graphs
• Equivariant Dimensions of Graph C*-algebras