Atomic Representations of Rank 2 Graph Algebras

Details Atomic Representations of Rank 2 Graph Algebras Atomic Representations of Rank 2 Graph Algebras

2007-05-31

arxiv.org/abs/0705.4498v2

J. Funct. Anal. 255 (2008), 819--853

Mathematics

Operator Algebras

42 pages, 5 figures

Scientific paper

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.

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