Homology of Yang-Baxter modules

2025/05/06 by Xiao Wang, Tian, Yin, Yuxin Zhang +2
Mathematics · #16T25 #57K10 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2505.03465

openalex publication_date 2025/05/06 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

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.

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