Journal of Lie Theory

no. 2
Structures of Nichols (Braided) Lie Algebras of Diagonal Type
Journal of Lie Theory, Volume 28 (2018) no. 2, pp. 357-380
\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 $\dim V=2$.
DOI: 10.5802/jolt.1006
Classification: 16W30, 16G10
Keywords: Braided vector space, Nichols algebra, Nichols braided Lie algebra, graph 
@article{JOLT_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--380},
     year = {2018},
     volume = {28},
     number = {2},
     doi = {10.5802/jolt.1006},
     zbl = {1391.16038},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1006/}
}
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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, Volume 28 (2018) no. 2, pp. 357-380. doi: 10.5802/jolt.1006

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