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∞ю(AG)
K0-Groups of AG
Biography
Ilwoo Cho
