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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Lexicographic TAF Algebras


Authors: Justin R. Peters and Yiu Tung Poon
Journal: Trans. Amer. Math. Soc. 349 (1997), 4825-4855
MSC (1991): Primary 46M40, 47D25; Secondary 06F25
MathSciNet review: 1443887
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Abstract: Lexicographic TAF algebras constitute a class of triangular AF
algebras which are determined by a countable ordered set $\Omega $, a dimension function, and a third parameter. While some of the important examples of TAF algebras belong to the class, most algebras in this class have not been studied. The semigroupoid of the algebra, the lattice of invariant projections, the Jacobson radical, and for some cases the automorphism group are computed. Necessary and sufficient conditions for analyticity are given. The results often involve the order properties of the set $\Omega $.


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Additional Information

Justin R. Peters
Affiliation: Department of Mathematics, Iowa State University, Ames, Iowa 50011-2064
Email: peters@iastate.edu

Yiu Tung Poon
Affiliation: Department of Mathematics, Iowa State University, Ames, Iowa 50011-2064
Email: ytpoon@iastate.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-97-02040-0
PII: S 0002-9947(97)02040-0
Received by editor(s): November 27, 1995
Article copyright: © Copyright 1997 American Mathematical Society