By Ilwoo Cho

ISBN-10: 146659019X

ISBN-13: 9781466590199

This publication introduces the learn of algebra caused via combinatorial gadgets known as directed graphs. those graphs are used as instruments within the research of graph-theoretic difficulties and within the characterization and answer of analytic difficulties. The booklet offers contemporary learn in operator algebra conception attached with discrete and combinatorial mathematical gadgets. It additionally covers instruments and strategies from a number of mathematical components, together with algebra, operator conception, and combinatorics, and provides quite a few functions of fractal thought, entropy idea, *K*-theory, and index theory.

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Radcliffe, Rigidity of Graph Products of Groups, Alg & Geom. Topology, Vol 3, (2003) 1079–1088. Voiculescu, K. Dykemma and A. Nica, Free Random Variables, CRM Monograph Series Vol 1 (1992). I. Cho, Diagram Groupoids and von Neumann Algebras Algebras, (2010) Submitted to Compl. Anal. Oper. Theo. I. Cho, Graph von Neumann Algebras, ACTA. Appl. , 95, (2007) 95–134. I. Cho, Characterization of Amalgamated Free Blocks of a Graph von Neumann Algebra, Compl. Anal. Oper. , 1, (2007) 367–398. I. Cho, Graph Groupoids and Partial Isometries, ISBN: 978-3-8383-1397-9 (2009) Lambert Academic Publisher.

Appl. , 95, (2007) 95–134. I. Cho, Characterization of Amalgamated Free Blocks of a Graph von Neumann Algebra, Compl. Anal. Oper. , 1, (2007) 367–398. I. Cho, Graph Groupoids and Partial Isometries, ISBN: 978-3-8383-1397-9 (2009) Lambert Academic Publisher. I. Cho, Operator Algebraic Quotient Structures Induced by Directed Graphs, Compl. Anal. Oper. , (2009) In Press. I. Cho, Vertex-Compressed Subalgebras of a Graph von Neumann Algebra, ACTA. Appl. , 108, (2009) 315–351. I. Cho, C-Valued Free Probability on Graph von Neumann Algebras, J.

A. Connes, Non-Commutative Geometry and the Spectral Model of Space-time, Quantum Spaces, Prog. Math. , 53, (2007) 203–227. A. Connes, M. Marcolli, Noncommutative Geometry, Quantum Fields and Motives, Amer. Math. , 55, ISBN: 978-0-8218-4210-2, (2008) AMS. 5 Bibliography 43 A. Connes, M. Marcolli, A Walk in the Noncommutative Garden, An Invitation to Noncommutative Geometry, World Sci. , MR2408150, (2008) 1–128. C. Correia Ramos, N. Martin, P. R. Pinto, and J. Sousa Ramos, Cuntz-Krieger Algebras Representations from Orbits of Interval Maps, J.

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