Homology of Yang-Baxter modules

TL;DR

This paper investigates the homology associated with Yang-Baxter operators derived from quantum groups, providing explicit decompositions and computations for specific modules, advancing understanding of algebraic structures in quantum algebra.

Contribution

It offers a direct sum decomposition of the Yang-Baxter chain complex and explicit homology computations for certain modules, a novel approach in quantum algebra.

Findings

Explicit chain complex decomposition for Yang-Baxter homology

Homology computed for specific $V_m$-modules

Enhanced understanding of algebraic structures in quantum groups

Abstract

We study the Yang-Baxter operator for the vector representation $V_m$ of the quantum group $U_q(sl_m)$. We consider the one-term Yang-Baxter homology with coefficients in $V_m$-modules and provide a direct sum decomposition of the one term Yang-Baxter chain complex. The homology is explicitly computed for some specific $V_m$-modules.