Bicharacters, braids and Jacobi identity

Jerzy Rozanski

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arXiv · q-alg/9611029

Bicharacters, braids and Jacobi identity

Jerzy Rozanski

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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 $E\in\End(A)$ and n-ary operations $Ω^{n}_{E}$ on A. Our result states that if $E(1)=0,E^{2}=0$ and $Ω^{3}_{E}=0$ then a braided Jacobi identity holds and the linear map E is a braided derivation of a braided Lie algebra.

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BibTeX RIS

Jerzy Rozanski. 1996-11-22. Bicharacters, braids and Jacobi identity. https://arxiv.org/abs/q-alg/9611029

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