Warped Products and Yang-Mills equations on non commutative spaces

Abstract

This paper presents a non self-dual solution of the Yang-Mills equations on a non commutative version of the classical $R_q^4\backslash \{0\}$, so generalizing the classical meron solution first introduced by de Alfaro, Fubini and Furlan in 1976. The basic tool for that is a generalization to non commutative spaces of the classical notion of warped products between metric spaces.

18 pages

References in corpus (6)

• Anti-selfdual Connections on the Quantum Projective Plane: Monopoles
• The ADHM Construction of Instantons on Noncommutative Spaces
• Dimensional reduction over the quantum sphere and non-abelian q-vortices
• (A class of) Hodge duality operators over the quantum SU(2)
• q-Quaternions and q-deformed su(2) instantons
• Differential and Twistor Geometry of the Quantum Hopf Fibration

Cited by in corpus (2)

• Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces
• A Hodge - De Rham Dirac operator on the quantum $\mathrm{SU}(2)$