Graph algebras
著者
書誌事項
Graph algebras
（Regional conference series in mathematics, no. 103）
Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society with support from the National Science Foundation, c2005
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注記
"NSF-CBMS Regional Research Conference on Graph Algebras: Operator Algebras We Can See, held at the University of Iowa, May 31-June 4, 2004"--T.p. verso
Includes bibliographical references (p. 105-110) and index
内容説明・目次
内容説明
Graph algebras are a family of operator algebras which are associated to directed graphs. These algebras have an attractive structure theory in which algebraic properties of the algebra are related to the behavior of paths in the underlying graph. In the past few years there has been a great deal of activity in this area, and graph algebras have cropped up in a surprising variety of situations, including non-abelian duality, non-commutative geometry, and the classification of simple $C^*$-algebras.The first part of the book provides an introduction to the subject suitable for students who have seen a first course on the basics of $C^*$-algebras. In the second part, the author surveys the literature on the structure theory of graph algebras, highlights some applications of this theory, and discusses several recent generalizations which seem particularly promising. The volume is suitable for graduate students and research mathematicians interested in graph theory and operator algebras.
目次
Introduction Directed graphs and Cuntz-Krieger families Uniqueness theorems for graph algebras Proofs of the uniqueness theorems Simplicity and ideal structure Arbitrary graphs Applications to non-abelian duality $K$-theory of graph algebras Cuntz-Pimsner algebras Topological graphs Higher-rank graphs Background material Bibliography Index.
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