A Hodge - De Rham Dirac operator on the quantum ${\rm SU}(2)$
Fabio Di Cosmo, Giuseppe Marmo, Juan Manuel P\'erez-Pardo, Alessandro, Zampini
TL;DR
This paper explores the construction of a Hodge-de Rham Dirac operator acting on the exterior algebra of quantum SU(2), providing a framework for analyzing differential structures in noncommutative geometry.
Contribution
It introduces a method to describe irreducible actions of the Hodge-de Rham Dirac operator on quantum SU(2) with a three-dimensional covariant calculus.
Findings
Explicit construction of the Dirac operator on quantum SU(2)
Demonstration of irreducible actions on the exterior algebra
Advancement in noncommutative geometric analysis
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 equipped with a three dimensional left covariant calculus.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Operator Algebra Research