Bicharacters, braids and Jacobi identity

1996/11/22 by Jerzy Różański, Jerzy Rozanski, Rozanski, Jerzy
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9611029

5 pages in LaTeX2e

arxiv created 1996/11/22 · openalex publication_date 1996/11/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an abelian group G we consider braiding in a category of G-graded modules M^kG given by a bicharacter χon G. For (G,χ)-bialgebra A in M^kG an analog of Lie bracket is defined. This bracket is determined by a linear map E∈\End(A) and n-ary operations Ωⁿ_E on A. Our result states that if E(1)=0,E²=0 and Ω³_E=0 then a braided Jacobi identity holds and the linear map E is a braided derivation of a braided Lie algebra.

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