dorsal/arxiv
View SchemaBicharacters, braids and Jacobi identity
| Authors | Jerzy Rozanski |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9611029 |
| URL | https://arxiv.org/abs/q-alg/9611029 |
Abstract
For an abelian group G we consider braiding in a category of G-graded modules $M^{kG}$ given by a bicharacter \chi on G. For $(G,\chi)$-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 $\Omega^{n}_{E}$ on A. Our result states that if $E(1)=0,E^{2}=0$ and $\Omega^{3}_{E}=0$ then a braided Jacobi identity holds and the linear map E is a braided derivation of a braided Lie algebra.
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"abstract": "For an abelian group G we consider braiding in a category of G-graded modules\n$M^{kG}$ given by a bicharacter \\chi on G. For $(G,\\chi)$-bialgebra A in\n$M^{kG}$ an analog of Lie bracket is defined. This bracket is determined by a\nlinear map $E\\in\\End(A)$ and n-ary operations $\\Omega^{n}_{E}$ on A. Our result\nstates that if $E(1)=0,E^{2}=0$ and $\\Omega^{3}_{E}=0$ then a braided Jacobi\nidentity holds and the linear map E is a braided derivation of a braided Lie\nalgebra.",
"arxiv_id": "q-alg/9611029",
"authors": [
"Jerzy Rozanski"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Bicharacters, braids and Jacobi identity",
"url": "https://arxiv.org/abs/q-alg/9611029"
},
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