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THE NATURAL MORPHISMS BETWEEN TOEPLITZ ALGEBRAS ON DISCRETE GROUPS

Published online by Cambridge University Press:  01 April 2000

QINGXIANG XU
QINGXIANG XU
Affiliation:
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China; [email protected]
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Abstract

Let G be a discrete group and (G, G+) be a quasi-ordered group. Set G0+ = G+∩(G+)−1 and G1 = (G+[setmn ]G0+)∪{e}. Let [Fscr ]G1(G) and [Fscr ]G+(G) be the corresponding Toeplitz algebras. In the paper, a necessary and sufficient condition for a representation of [Fscr ]G+(G) to be faithful is given. It is proved that when G is abelian, there exists a natural C*-algebra morphism from [Fscr ]G1(G) to [Fscr ]G+(G). As an application, it is shown that when G = ℤ2 and G+ = ℤ+ × ℤ, the K-groups K0([Fscr ]G1(G)) ≅ ℤ2, K1([Fscr ]G1(G)) ≅ ℤ and all Fredholm operators in [Fscr ]G1(G) are of index zero.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 593 - 603
Copyright
The London Mathematical Society 2000

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