Classifying Higher Rank Analytic Toeplitz Algebras

2006/04/28 by Stephen C Power, Power, Stephen C
Mathematics · #47L55 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:47L55

paper · pdf · doi:10.48550/arxiv.math/0604630

Includes comment on related joint work with Baruch Solel and minor changes. 35 pages.

arxiv created 2007/04/01 · arxiv updated 2009/12/01

Abstract

To a higher rank directed graph (Λ, d), in the sense of Kumjian and Pask, one can associate natural noncommutative analytic Toeplitz algebras, both weakly closed and norm closed. We introduce methods for the classification of these algebras in the case of single vertex graphs.

Related

• Realising the Toeplitz algebra of a higher-rank graph as a Cuntz-Krieger algebra
• Construction of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials
• Topological higher-rank graphs and the C^*-algebras of topological 1-graphs
• Factoring in Non-commutative Analytic Toeplitz Algebras
• Kumjian-Pask algebras of higher-rank graphs