The Index Semigroup Induced by Finite Trees: Index Morphisms and Classification of von Neumann Algebras Induced by Finite Trees

Cho, Ilwoo

ISBN 10: 3846590150 / ISBN 13: 9783846590157

Published by LAP LAMBERT Academic Publishing, 2011

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Bibliographic Details

• Title: The Index Semigroup Induced by Finite Trees: Index Morphisms and Classification of von Neumann Algebras Induced by Finite Trees
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2011
• Language: English
• ISBN 10: 3846590150
• ISBN 13: 9783846590157
• Binding: Paperback
• Condition: Like New
• Book Type: book

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Synopsis

In this monograph, we study graph-index, Watatani's extended Jones index, and the relations between them. From this investigation, we realize that graph-index of graphs and Jones index of von Neumann algebras generated by "graph groupoids" are equivalent in a certain sense, whenver given graphs are finite trees. We provides the classification of graph-groupoid von Neumann algebras induced by finite trees with respect to these equivalent indexes. By understanding the indexings as morphisms, we establish actions of morphisms and construct the corresponding algebraic structure, called the "index semigroup." We study the fundamental properties of them. As application, we consider the connection between our index semigroup and K-groups of finite-tree-groupoid von Neumann algebras.

About the Author

Master Degrees: Sungkyunkwan University and University of Iowa (Math) / Ph.D : University of Iowa (Math) / Current Position: Assistant Professor in Saint Ambrose University