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arXiv · 1310.6723

Divided difference operators in equivariant $KK$-theory

Ho-Hon Leung
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Abstract

Let $G$ be a compact connected Lie group with a maximal torus $T$. Let $A$, $B$ be $G$-$\mathrm{C}^\ast$-algebras. We define certain divided difference operators on Kasparov's $T$-equivariant $KK$-group $KK_T(A,B)$ and show that $KK_G(A,B)$ is a direct summand of $KK_T(A,B)$. More precisely, a $T$-equivariant $KK$-class is $G$-equivariant if and only if it is annihilated by an ideal of divided difference operators. This result is a generalization of work done by Atiyah, Harada, Landweber and Sjamaar.

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Ho-Hon Leung. 2013-10-24. Divided difference operators in equivariant $KK$-theory. https://doi.org/10.1142/s1793525314500071

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