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Toeplitz Algebras on Strongly Pseudoconvex Domains

Published online by Cambridge University Press:  11 January 2016

Guangfu Cao
Guangfu Cao*
Affiliation:
Department of Mathematics, Guangzhou University, Guangzhou 510006, China, [email protected]
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Abstract

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In the present paper, it is proved that the K0-group of a Toeplitz algebra on any strongly pseudoconvex domain is always isomorphic to the K0-group of the relative continuous function algebra, and is thus isomorphic to the topological K0-group of the boundary of the relative domain. Further there exists a ring isomorphism between the K0-groups of Toeplitz algebras and the Chern classes of the relative boundaries of strongly pseudoconvex domains. As applications of our main result, K-groups of Toeplitz algebras on some special strongly pseudoconvex domains are computed. Our results show that the Toeplitz algebras on strongly pseudoconvex domains have rich structures, which deeply depend on the topological structures of relative domains. In addition, the first cohomology groups of Toeplitz algebras are also computed.

Keywords

47B35
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 185 , 2007 , pp. 171 - 186
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

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