### Abstract

We construct $\theta$-deformations $A(SL_\theta(2,\mathbb{H}))$, $A(Sp_\theta(2))$ of the corresponding classical groups.

Starting from the basic instanton on a noncommutative four-sphere $S^4_\theta$, we construct a noncommutative family of instantons parametrized by the quantum quotient of $A(SL_\theta(2,\mathbb{H}))$ by $A(Sp_\theta(2))$.

Based on joint work with Giovanni Landi (University of Trieste), Cesare Reina (SISSA, Trieste), Walter van Suijlekom (MPI, Bonn).