Operations on Graphs, Groupoids, and Operator Algebras: Operations on Graph-Depending Structures - Couverture souple

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9783838352718: Operations on Graphs, Groupoids, and Operator Algebras: Operations on Graph-Depending Structures
Couverture souple
ISBN 10 : 3838352718 ISBN 13 : 9783838352718
Editeur : LAP Lambert Academic Publishing, 2010

Synopsis

In this monograph, we consider natural operations on directed graphs. And we find the connections between our operations on graphs and the groupoid-perations on "graph" groupoids. Remark that we cannot guarantee the (algebraic or categorial) groupoids generated by the grouopoid-operations; sum, product, quotient or complement; of graph groupoids are again graph groupoids. By defining suitable operations on graphs, we can conclude the groupoids generated by the groupoid-operations of graph groupoids are again graph groupoids; for example, the product groupoid of two graph groupoids is groupoid-isomorphic to the graph groupoid of the product graph, etc. This provides another bridge connceting combinatorics and algebra. Recently, the von Neumann algebras generated by graph groupoids, called graph von Neumann algebras, have been studied. By using the fundamental techniques from graph von Neumann algebra theory, we can characterize the properties of groupoid von Neumann algebras, generated by groupoids obtained from the groupoid-operations, as certain graph 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 consider natural operations on directed graphs. And we find the connections between our operations on graphs and the groupoid-perations on "graph" groupoids. Remark that we cannot guarantee the (algebraic or categorial) groupoids generated by the grouopoid-operations; sum, product, quotient or complement; of graph groupoids are again graph groupoids. By defining suitable operations on graphs, we can conclude the groupoids generated by the groupoid-operations of graph groupoids are again graph groupoids; for example, the product groupoid of two graph groupoids is groupoid-isomorphic to the graph groupoid of the product graph, etc. This provides another bridge connceting combinatorics and algebra. Recently, the von Neumann algebras generated by graph groupoids, called graph von Neumann algebras, have been studied. By using the fundamental techniques from graph von Neumann algebra theory, we can characterize the properties of groupoid von Neumann algebras, generated by groupoids obtained from the groupoid-operations, as certain graph von Neumann algebras.

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
2010
Langue
anglais
ISBN 10 
3838352718
ISBN 13 
9783838352718
Reliure
Broché
Nombre de pages
112
Coordonnées du fabricant
non disponible
Personne responsable
KreGa Onlinehandel GmbH
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