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Bivariant $K$-theory and the Weyl algebra

Joachim Cuntz
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Abstract

We introduce a new version $kk^{\rm alg}$ of bivariant $K$-theory that is defined on the category of all locally convex algebras. A motivating example is the Weyl algebra $W$, i.e. the algebra generated by two elements satisfying the Heisenberg commutation relation, with the fine locally convex topology. We determine its $kk^{\rm alg}$-invariants using a natural extension for $W$. Using similar methods the $kk^{\rm alg}$-invariants can be determined for many other algebras of similar type.

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Joachim Cuntz. 2004-07-19. Bivariant $K$-theory and the Weyl algebra. https://arxiv.org/abs/math/0401295

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