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An Application of Higher Traces

Part of the Operator Theory: Advances and Applications book series (OT, volume 183)

Abstract

Let
$$ P = \sum\limits_g {T\left( g \right)P\left( g \right):C^\infty \left( {M,\mathbb{C}^N } \right) \to C^\infty \left( {M,\mathbb{C}^N } \right)} $$
(13.1)
be a nonlocal elliptic operator with shifts generating the group Г. Suppose that P is a projection; i.e.,
$$ P = P^ * = P^2 . $$
Let us define its index
$$ ind_\Lambda P \in K_1 \left( \Lambda \right) $$
(13.2)
with values in the odd K-group of the group C*-algebra Λ = C*(Г). This can be done, for example, as follows.

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Copyright information

© Birkhäuser Verlag AG 2008

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