Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bicharacters, braids and Jacobi identity   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.

15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th