Quantum Clifford-Hopf Algebras for Even Dimensions

TL;DR

This paper introduces quantum Clifford-Hopf algebras for even dimensions, deriving their R-matrices as elliptic solutions to the Yang-Baxter equation, and explores their connections to supersymmetry and spin chain models.

Contribution

It presents the construction of quantum Clifford-Hopf algebras for even dimensions and derives their elliptic R-matrices, linking them to supersymmetry and generalized spin chain models.

Findings

Derived elliptic R-matrices solving Yang-Baxter equation.

Connected algebraic structures to supersymmetry extensions.

Analyzed spin chain Hamiltonians related to Suzuki's model.

Abstract

In this paper we study the quantum Clifford-Hopf algebras $\widehat{CH_q(D)}$ for even dimensions $D$ and obtain their intertwiner $R-$matrices, which are elliptic solutions to the Yang- Baxter equation. In the trigonometric limit of these new algebras we find the possibility to connect with extended supersymmetry. We also analyze the corresponding spin chain hamiltonian, which leads to Suzuki's generalized $XY$ model.