Algebras, Graphs and Their Applications

Algebras, Graphs and Their Applications

By: Ilwoo Cho (author)Hardback

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Description

This book introduces the study of algebra induced by combinatorial objects called directed graphs. These graphs are used as tools in the analysis of graph-theoretic problems and in the characterization and solution of analytic problems. The book presents recent research in operator algebra theory connected with discrete and combinatorial mathematical objects. It also covers tools and methods from a variety of mathematical areas, including algebra, operator theory, and combinatorics, and offers numerous applications of fractal theory, entropy theory, K-theory, and index theory.

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Contents

Algebra on Graphs Introduction Preliminaries Groupoids under Operations Operations on Graphs Representations and Operator Algebras of Graph Groupoids Introduction Partial Isometries Graph von Neumann Algebras M-Diagonal Graph W*-Probability Spaces C*-Subalgebras Generated by Partial Isometries Operator Theory on Graphs Introduction Self-Adjointness and Unitarity Normality of Graph Operators Operators in Free Group Factors Graph Operators Induced by Regular Trees Fractal on Graph Groupoids Introduction Labeled Graph Groupoids and Graph Automata Graph Fractaloids Labeling Operators of Graph Fractaloids Graph-Theoretical Characterization Fractal Graphs Constructed by Fractal Graphs Fractal Pairs of Graph Fractaloids Equivalence Classes of Graph Fractaloids Completely Finite Fractalization Fractalized-Graph von Neumann Algebras Fractalized Labeling Operators Entropy Theory on Graphs Entropy Entropy on Finite Graphs Entropy of Finite Fractal Graphs Jones Index Theory on Graph Groupoids Introduction Quotient Graphs and Graph Index Watatani's Extended Jones Index Theory Index Theory on Graph von Neumann Algebras Basic Construction Induced by Full-Vertex Subgraph Inclusion Ladders and Nets on Graph von Neumann Algebras Index-Morphisms Network Theory on Graphs Electric Resistance Network Theory Representations of ERNs ERN-Actions on Energy Hilbert Spaces Free Structures Induced by ERN-Groupoids K-Theory on Graphs Introduction K-Theory Projections in AG Projections in M (AG) K0-Groups of AG

Product Details

  • publication date: 10/09/2013
  • ISBN13: 9781466590199
  • Format: Hardback
  • Number Of Pages: 444
  • ID: 9781466590199
  • weight: 771
  • ISBN10: 146659019X

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