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Operations on Graphs, Groupoids, and Operator Algebras (Paperback)
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Operations on Graphs, Groupoids, and Operator Algebras (Paperback)
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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.
General
Imprint: |
Lap Lambert Academic Publishing
|
Country of origin: |
Germany |
Release date: |
June 2010 |
First published: |
June 2010 |
Authors: |
Ilwoo Cho
|
Dimensions: |
229 x 152 x 7mm (L x W x T) |
Format: |
Paperback - Trade
|
Pages: |
112 |
ISBN-13: |
978-3-8383-5271-8 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
General
|
LSN: |
3-8383-5271-8 |
Barcode: |
9783838352718 |
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