Nonself-adjoint 2-graph algebras

Abstract

We study the structure of weakly-closed nonself-adjoint algebras arising from representations of single vertex 2-graphs. These are the algebras generated by 2 isometric tuples which satisfy a certain commutation relation. We show that these algebras have a lower-triangular $3\times 3$ form. The left-hand side of this matrix decomposition is a slice of the enveloping von Neumann algebra generated by the 2-graph algebra. We further give necessary and sufficient conditions for these algebras themselves to be von Neumann algebras. The paper concludes with further study of atomic representations.

29 pages

References in corpus (5)

• Free Semigroupoid Algebras
• Representations of Higher Rank Graph Algebras
• Classifying Higher Rank Analytic Toeplitz Algebras
• Dilation Theory for Rank 2 Graph Algebras
• Finitely Correlated Representations of Product Systems of $C^{\ast }$-Correspondences over ${\mathbb{N}}^k$

Cited by in corpus (1)

• Factoriality and type classification of \textsf{k}-graph von Neumann algebras