Noncommutative families of instantons

TL;DR

This paper develops noncommutative deformations of classical groups and constructs a quantum family of charge 1 instantons on a noncommutative four-sphere, expanding the framework of instanton moduli in noncommutative geometry.

Contribution

It introduces $ heta$-deformations of SL(2,H) and Sp(2), and constructs a noncommutative family of instantons parametrized by a quantum quotient, advancing noncommutative instanton theory.

Findings

Constructed $ heta$-deformations of SL(2,H) and Sp(2)

Developed a noncommutative family of instantons of charge 1

Parametrized the family by a quantum quotient of deformed groups

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 $Sp_\theta(2)$.