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C*-Algebras of inverse semigroups

Published online by Cambridge University Press:  20 January 2009

J. Duncan  and
A. L. T. Paterson
J. Duncan
Affiliation:
Indiana University and University of Stirling
A. L. T. Paterson
Affiliation:
University of Aberdeen
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There are various algebras which may be associated with a discrete group G. In particular we may consider the complex group ring ℂG, the convolution Banach algebra l1(G), the enveloping C*-algebra C*(G) of l1(G), and the reduced C*-algebra determined by the completion of l1(G) under the left regular representation on l2(G). There is a substantial literature on the circle of ideas associated with the embeddings

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 28 , Issue 1 , February 1985 , pp. 41 - 58
Copyright
Copyright © Edinburgh Mathematical Society 1985

References

REFERENCES

1.Barnes, B. A., Representations of the l 1-algebra of an inverse semigroup, Trans. Amer. Math. Soc. 218 (1976), 361–196.Google Scholar
2.Barnes, B. A., Representations of the l 1-algebra of an inverse semigroup having the separation property, Glasgow Math. J. 18 (1977), 131–143.CrossRefGoogle Scholar
3.Duncan, J. and Namioka, I., Amenability of inverse semigroups and their semigroup algebras, Proc. Roy. Soc. Edinburgh 80A (1978), 309–321.CrossRefGoogle Scholar
4.Howie, J. M., An introduction to semigroup theory (Academic Press, London, 1976).Google Scholar
5.McAlister, D. B., A random ramble through inverse semigroups, Semigroups (edited by Hall, T. E., Hones, P. R. and Preston, G. B.) (Academic Press, New York, 1980), 1–25.Google Scholar
6.Munn, W. D., Regular ω-semigroups, Glasgow Math. J. 9 (1968), 46–66.Google Scholar
7.Palmer, T. W., Monograph on general *-algebras; in preparation.Google Scholar
8.Paterson, A. L. T., Weak containment and Clifford semigroups, Proc. Roy. Soc. Edinburgh 81A (1978), 23–30.CrossRefGoogle Scholar
9.Sakai, S., C*-algebras and W*-algebras (Springer, Berlin, 1971).Google Scholar
10.Wordingham, J. R., The left regular *-representation of an inverse semigroup, Proc. Amer. Math. Soc. 86 (1982), 55–58.Google Scholar
11.Wordingham, J. R., Topics in semigroup algebras (Ph.D. thesis, University of Stirling, 1982).Google Scholar