2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69929We 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.This version contains corrections to misprints and minor inaccuracies as well as some additional commentsK-Theory and HomologyMathematical Physics19L99 16W99text