Noncommutative families of instantons

Abstract

We construct $\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\theta(2,H)$ by $Sp_\theta(2)$.