k-deformed Poincare algebras and quantum Clifford-Hopf algebras

TL;DR

This paper explores the mathematical structure of k-deformed Poincare algebras and their relation to quantum Clifford-Hopf algebras, revealing connections to deformed anti-de Sitter algebra within a topological framework.

Contribution

It introduces a novel algebraic framework linking k-deformed Poincare algebras with quantum Clifford-Hopf structures and extends the Atiyah-Bott-Shapiro theorem to this context.

Findings

Equivalence to deformed anti-de Sitter algebra U_q(so(3,2))

Extension of Atiyah-Bott-Shapiro theorem to quantum Clifford algebras

New insights into the algebraic structure of quantum spacetime symmetries

Abstract

The Minkowski spacetime quantum Clifford algebra structure associated with the conformal group and the Clifford-Hopf alternative k-deformed quantum Poincare algebra is investigated in the Atiyah-Bott-Shapiro mod 8 theorem context. The resulting algebra is equivalent to the deformed anti-de Sitter algebra U_q(so(3,2)), when the associated Clifford-Hopf algebra is taken into account, together with the associated quantum Clifford algebra and a (not braided) deformation of the periodicity Atiyah-Bott-Shapiro theorem.