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Lexicographic semigroupoids

Published online by Cambridge University Press:  19 September 2008

S. C. Power
S. C. Power
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England
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Abstract

The natural lexicographic semigroupoids associated with Cantor product spaces indexed by countable linear orders are classified. Applications are given to the classification of triangular operator algebras which are direct limits of upper-triangular matrix algebras.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 2 , April 1996 , pp. 365 - 377
Copyright
Copyright © Cambridge University Press 1996

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References

REFERENCES

[1]Arveson, W. B.. Analyticity in operator algebras. Amer. J. Math. 89 (1967), 578–642.Google Scholar
[2]Donsig, A. P.. Semisimple triangular AF algebras. J. Functional Anal. 111 (1993), 323–349.CrossRefGoogle Scholar
[3]Donsig, A. P. and Hopenwasser, A.. Order preservation in limit algebras. J. Functional Anal. 133 (1995), 342–394.Google Scholar
[4]Hopenwasser, A. and Power, S. C.. Classification of limits of triangular matrix algebras. Proc. Edinburgh Math. Soc. 36 (1992), 107–121.CrossRefGoogle Scholar
[5]Muhly, P. S. and Solel, b.. Subalgebras of groupoid C*-algebras. J. für die Reine und Ange. Math. 402 (1989), 41–75.Google Scholar
[6]Poon, Y. T.. A complete isomorphism invariant for a class of triangular UHF algebras. J. Operator Th. 27 (1992), 221–230.Google Scholar
[7]Power, S. C.. Limit algebras: an introduction to subalgebras of C*-algebras. Pitman Research Notes in Mathematics vol 278. Longman Scientific and Technical, London-New York, 1992.Google Scholar
[8]Power, S. C.. On the outer automorphism groups of triangular alternation limit algebras. J. Functional Anal. 113 (1993), 462–471.Google Scholar
[9]Power, S. C.. Infinite lexicographic products of triangular algebras. Bull. London Math. Soc. 27 (1995), 273–277.CrossRefGoogle Scholar
[10]Renault, J.. A groupoid approach to C*-algebras. Lecture Notes in Math. 793. Springer, Berlin-Heidelberg-New York, 1980.Google Scholar