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Exact Sequences for the Kasparov Groups of Graded Algebras

Published online by Cambridge University Press:  20 November 2018

George Skandalis
George Skandalis*
Affiliation:
Queen's University, Kingston, Ontario
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In [11] G. G. Kasparov defined the “operator K-functor” KK(A, B) associated with the graded C*-algebras A and B. If the algebras A and B are trivially graded and A is nuclear he proves six term exact sequence theorems. He asks whether this extends to the graded case.

Here we prove such “six-term exact sequence” results in the graded case. Our proof does not use nuclearity of the algebra A. This condition is replaced by a completely positive lifting condition (Theorem 1.1).

Using our result we may extend the results by M. Pimsner and D. Voiculescu on the K groups of crossed products by free groups to KK groups [15]. We give however a different way of computing these groups using the equivariant KK-theory developed by G. G. Kasparov in [12]. This method also allows us to compute the KK groups of crossed products by PSL2(Z).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 37 , Issue 2 , 01 April 1985 , pp. 193 - 216
Copyright
Copyright © Canadian Mathematical Society 1985

References

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