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

Cho, Ilwoo

 
9783846590157: The Index Semigroup Induced by Finite Trees: Index Morphisms and Classification of von Neumann Algebras Induced by Finite Trees
Couverture souple
ISBN 10 : 3846590150 ISBN 13 : 9783846590157
Editeur : LAP LAMBERT Academic Publishing, 2011

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Biographie de l'auteur

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

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2011
Langue
anglais
ISBN 10 
3846590150
ISBN 13 
9783846590157
Reliure
Broché
Nombre de pages
88
Coordonnées du fabricant
non disponible
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