Bivariant $K$-theory and the Weyl algebra

Abstract

We introduce a new version $k{k}^{\mathrm{alg}}$ 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 $k{k}^{\mathrm{alg}}$-invariants using a natural extension for $W$. Using similar methods the $k{k}^{\mathrm{alg}}$-invariants can be determined for many other algebras of similar type.

This version contains corrections to misprints and minor inaccuracies as well as some additional comments

Cited by in corpus (2)

• The Thom isomorphism in bivariant K-theory
• Noncommutative stable homotopy theory