Geodesic
Structures of Nichols (Braided) Lie Algebras of Diagonal Type
Journal of Lie theory, Tome 28 (2018) no. 2, pp. 357-38 Cet article a éte moissonné depuis la source Heldermann Verlag

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\def\B{{\frak B}} \def\L{{\frak L}} Let $V$ be a braided vector space of diagonal type. Let $\B(V)$, $\L^-(V)$ and $\L(V)$ be the Nichols algebra, Nichols Lie algebra and Nichols braided Lie algebra over $V$, respectively. We show that a monomial belongs to $\L(V)$ if and only if this monomial is connected. We obtain the basis for $\L(V)$ of arithmetic root systems and the dimension of $\L(V)$ of finite Cartan type. We give the sufficient and necessary conditions for $\B(V) = F\oplus \L^-(V)$ and $\L^-(V)= \L(V)$. We obtain an explicit basis for $\L^ - (V)$ over the quantum linear space $V$ with $\dim V=2$.
Classification : 16W30, 16G10
Mots-clés : Braided vector space, Nichols algebra, Nichols braided Lie algebra, graph 
@article{JLT_2018_28_2_JLT_2018_28_2_a3,
     author = {W. Wu and J. Wang and S. Zhang and Y.-Z. Zhang},
     title = {Structures of {Nichols} {(Braided)} {Lie} {Algebras} of {Diagonal} {Type}},
     journal = {Journal of Lie theory},
     pages = {357--38},
     year = {2018},
     volume = {28},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2018_28_2_JLT_2018_28_2_a3/}
}
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W. Wu; J. Wang; S. Zhang; Y.-Z. Zhang. Structures of Nichols (Braided) Lie Algebras of Diagonal Type. Journal of Lie theory, Tome 28 (2018) no. 2, pp. 357-38. http://geodesic.mathdoc.fr/item/JLT_2018_28_2_JLT_2018_28_2_a3/