A Hodge–de Rham Dirac operator on the quantum SU(2)

Abstract

We describe how it is possible to describe irreducible actions of the Hodge -de Rham Dirac operator upon the exterior algebra over the quantum spheres SUq(2) equipped with a three dimensional left covariant calculus.

Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces

“…When the commutative algebra of functions on two and three dimensional spheres is deformed within the quantum group setting, a Hodge duality on the corresponding exterior algebras has been studied in[11,51,49,50,30,29]. Within the Drinfeld -Jimbo deformation formalism we refer the reader to[12,1] and references therein for a consistent notion of a Hodge duality for a a differential calculus suitably given by a twist quantization.…”