On Quantum Deformations of D=4 Conformal Algebra

TL;DR

This paper constructs and classifies classical r-matrices for the sl(4,C) algebra, exploring their properties under reality conditions and their relation to quantum deformations of the conformal algebra in four dimensions.

Contribution

It introduces three classes of classical r-matrices for sl(4,C) using a quasi-Frobenius algebra approach, analyzing their CYBE solutions and reality conditions.

Findings

Three classes of r-matrices constructed with 8, 10, 12 generators

Reality conditions restrict to 8-dimensional matrices with full deformation parameters

All kappa-deformations satisfy CYBE, unlike in Poincare case

Abstract

Three classes of classical r-matrices for sl(4,C) algebra are constructed in quasi-Frobenius algebra approach. They satisfy CYBE and are spanned respectively on 8,10,12 generators. The o(4,2) reality condition can be imposed only on the eight dimensional r matrices with dimension-full deformation parameters. Contrary to the Poincare algebra case, it appears that all deformations with a mass-like deformation parameter (kappa- deformations) are described by classical r-matrices satisfying CYBE.