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Categorical constructions in C*-algebra theory

Part of: Selfadjoint operator algebras Methods of category theory in functional analysis General theory of categories and functors

Published online by Cambridge University Press:  09 April 2009

M. Khoshkam  and
J. Tavakoli
M. Khoshkam
Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan S7N 5E6, Canada e-mail: [email protected]
J. Tavakoli
Affiliation:
Science Department, SIFC, Regina Campus, Room 118, Regina SK S4S 0A2, Canada e-mail: [email protected]
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Abstract

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The notions of limits and colimits are studied in the category of C*-algebras. It is shown that limits and colimits of diagrams of C*-algebras are stable under tensor product by a fixed C*-algebra, and crossed product by a locally compact group.

Keywords

C*-algebrascategoriestensor productcrossed productlimitspullbackpushoutdiagram

MSC classification

Secondary: 46L05: General theory of $C^*$-algebras 18A25: Functor categories, comma categories 46M15: Categories, functors
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 73 , Issue 1 , August 2002 , pp. 97 - 114
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Dykema, K., ‘Exactness of reduced amalgamated free product C*-algebras’, preprint.Google Scholar
[2]Kirchberg, E. and Wassermann, A., ‘Exact groups and continuous bundles of C*-algebras’, preprint.Google Scholar
[3]Kirchberg, E. and Wassermann, A., ‘Permanence properties of C*-exact groups’, preprint.Google Scholar
[4]MacLane, S., Categories for working mathematicians (Springer, New York, 1972).Google Scholar
[5]Pedersen, G., C*-algebras and their automorphism groups (Academic Press, New York, 1979).Google Scholar
[6]Pedersen, G., ‘Pullback and pushout constructions in C*-algebra theory’, J. Funct. Anal. 167 (1999), 243–344.CrossRefGoogle Scholar
[7]Takesaki, M., Theory of operator algebras I (Springer, New York, 1979).CrossRefGoogle Scholar
[8]Voiculescu, D., Dykema, K. and Nica, A., Free random variables, CRM Monogr. Ser. 1 (AMS, Providence, RI, 1992).CrossRefGoogle Scholar
[9]Wassermann, S., ‘On tensor products of free-group C*-algebras’, Bull. London Math. Soc. 222 (1990), 375–380.CrossRefGoogle Scholar