Atomic representations of rank 2 graph algebras.

Davidson, Kenneth R. and Power, Stephen C. and Yang, Dilian (2008) Atomic representations of rank 2 graph algebras. Journal of Functional Analysis, 255 (4). pp. 819-853. ISSN 0022-1236

Abstract

We provide a detailed analysis of atomic *-representations of rank 2 graphs on a single vertex. They are completely classified up to unitary equivalence, and decomposed into a direct sum or direct integral of irreducible atomic representations. The building blocks are described as the minimal *-dilations of defect free representations modelled on finite groups of rank 2.