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2007 Toeplitz algebras on strongly pseudoconvex domains
Guangfu Cao
Nagoya Math. J. 185: 171-186 (2007).

Abstract

In the present paper, it is proved that the $K_{0}$-group of a Toeplitz algebra on any strongly pseudoconvex domain is always isomorphic to the $K_{0}$-group of the relative continuous function algebra, and is thus isomorphic to the topological $K^{0}$-group of the boundary of the relative domain. Further there exists a ring isomorphism between the $K_{0}$-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.

Citation

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Guangfu Cao. "Toeplitz algebras on strongly pseudoconvex domains." Nagoya Math. J. 185 171 - 186, 2007.

Information

Published: 2007
First available in Project Euclid: 23 March 2007

zbMATH: 1134.47056
MathSciNet: MR2301465

Subjects:
Primary: 47B35

Keywords: $K_{0}$-group , $K_{1}$-group , pseudoconvex domain , Toeplitz algebra

Rights: Copyright © 2007 Editorial Board, Nagoya Mathematical Journal

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