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Discrete product systems with twisted units

Published online by Cambridge University Press:  17 April 2009

Marcelo Laca
Marcelo Laca
Affiliation:
Department of Mathematics, The University of Newcastle, Newcastle NSW 2308, Australia, e-mail: marcelo@math.newcastle.edu.au
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Abstract

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The spectral C*-algebra of the discrete product systems of H.T. Dinh is shown to be a twisted semigroup crossed product whenever the product system has a twisted unit. The covariant representations of the corresponding dynamical system are always faithful, implying the simplicity of these crossed products; an application of a recent theorem of G.J. Murphy gives their nuclearity. Furthermore, a semigroup of endomorphisms of B(H) having an intertwining projective semigroup of isometries can be extended to a group of automorphisms of a larger Type I factor.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 2 , October 1995 , pp. 317 - 326
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Adji, S., Laca, M., Nilsen, M. and Raeburn, I., ‘Crossed products by semigroups of endo-morphisms and the Toeplitz algebras of ordered groups’, Proc. Amer. Math. Soc. 122 (1994), 1133–1141.Google Scholar
[2]Keswani, S. Boyd N. and Raeburn, I., ‘Faithful representations of crossed products by endomorphisms’, Proc. Amer. Math. Soc. 118 (1993), 427–436.Google Scholar
[3]Cuntz, J., ‘Simple C*-algebras generated by isometries’, Comm. Math. Phys. 57 (1977), 173–185.CrossRefGoogle Scholar
[4]Dinh, H.T., ‘Discrete product systems and their C*-algebras’, J. Funct. Anal. 102 (1991), 1–34.CrossRefGoogle Scholar
[5]Dinh, H.T.,‘On discrete semigroups of *-endomorphisms of Type I factors’, Internat. J. Math. 5 (1992), 609–628.CrossRefGoogle Scholar
[6]Dinh, H.T., ‘On generalized Cuntz C*-algebras’, J. Operator Theory (to appear).Google Scholar
[7]Laca, M. and Raeburn, I., ‘Extending multipliers from semigroups’, Proc. Amer. Math. Soc. 123 (1995), 355–362.Google Scholar
[8]Murphy, G.J., ‘Crossed products of C*-algebras by endomorphisms’, (preprint, 1994).Google Scholar
[9]Phillips, J. and Raeburn, I., ‘Semigroups of isometries, Toeplitz algebras and twisted crossed products’, Integral Equations Operator Theory 17 (1993), 579–602.CrossRefGoogle Scholar
[10]Raeburn, I., ‘On crossed products and Takai duality’, Proc. Edin. Math. Soc. 31 (1988), 321–330.CrossRefGoogle Scholar
[11]Stacey, P.J., ‘Crossed products of C*-algebras by *-endomorphisms’, J. Austral. Math. Soc. Ser. A 54 (1993), 204–212.Google Scholar