The Index Semigroup Induced by Finite Trees

Ilwoo Cho

ISBN 10: 3846590150 / ISBN 13: 9783846590157

Published by LAP LAMBERT Academic Publishing Dez 2011, 2011

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 88 pp. Englisch.

Seller Inventory # 9783846590157

Bibliographic Details

• Title: The Index Semigroup Induced by Finite Trees
• Publisher: LAP LAMBERT Academic Publishing Dez 2011
• Publication Date: 2011
• Language: English
• ISBN 10: 3846590150
• ISBN 13: 9783846590157
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 6D millimeters 220 millimeters width by 150 millimeters height by 6 millimeters depth
• Weight: 149 grams

About this title

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