Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Nonproduct type analytic TUHF algebras

Author: Belisario A. Ventura
Journal: Trans. Amer. Math. Soc. 346 (1994), 719-738
MSC: Primary 46L40; Secondary 46K50, 47D25
MathSciNet review: 1282898
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We construct examples of nonproduct type real valued cocycles on a UHF groupoid, and show that the analytic triangular algebras associated to those cocycles, can only correspond to nonproduct type cocycles.

References [Enhancements On Off] (What's this?)

  • [B] O. Bratteli, Crossed products of $ UHF$ algebras by product type actions, Duke Math. J. 46 (1979), 1-23. MR 523598 (82a:46063)
  • [DH] A. Donsig and T. Hudson, The ideal lattice of triangular $ AF$ algebras (work in progress).
  • [HR] D. Handelman and W. Rossmann, Actions of compact groups on $ AF$ $ {C^{\ast}}$-algebras, Illinois J. Math. 29 (1985), 51-95. MR 769758 (86f:46071)
  • [HP] A. Hopenwasser and J. Peters, Full nest algebras, Illinois J. Math. 38 (1994). MR 1269701 (95c:47047)
  • [K] A. Kishimoto, On the fixed point algebra of a $ UHF$ algebra under a periodic automorphism of product type, Publ. Res. Inst. Math. Sci. Kyoto 13 (1977), 777-791. MR 0500177 (58:17863)
  • [MS] P. Muhly and B. Solel, Subalgebras of groupoid $ {C^{\ast}}$-algebras, J. Reine Angew. Math. 402 (1989), 41-75. MR 1022793 (90m:46098)
  • [PPW1] J. Peters, Y. Poon and B. Wagner, Triangular $ AF$ algebras, J. Operator Theory 23 (1990), 81-114. MR 1054818 (91h:46102)
  • [PPW2] -, Analytic $ TAF$ algebras, Canad J. Math. 45 (1993), 1009-1031; Erratum, Canad. J. Math. 46 (1994), 395-396.
  • [P1] S. Power, Algebraic orders on $ {K_0}$ and approximtely finite operator algebras, J. Operator Theory 27 (1992), 87-106. MR 1241116 (95b:46100)
  • [P2] -, Limit algebras: an introduction to subalgebras of $ {C^{\ast}}$-algebras, Pitman Research Notes in Math. Ser., No. 278, Longman Scientific & Technical, UK, 1992.
  • [R] J. Renault, A groupoid approach to $ {C^{\ast}}$-algebras, Lecture Notes in Math., vol. 793, Springer-Verlag, Berlin, 1980. MR 584266 (82h:46075)
  • [S] B. Solel, Unpublished notes.
  • [V] B. Ventura, Strongly maximal triangular $ AF$ algebras, Internat. J. Math. 2 (1991), 567-598. MR 1124284 (92k:46096)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46L40, 46K50, 47D25

Retrieve articles in all journals with MSC: 46L40, 46K50, 47D25

Additional Information

Keywords: Nonproduct type cocycle, analytic triangular UHF algebras, UHF groupoid, nonproduct type automorphism
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society