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 $S_{\theta }^4$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $S{L}_{\theta }(2,H)$ by $S{p}_{\theta }(2)$.

v2: Minor changes; computation of the pairing at the end of Sect. 5.1 improved