Journal of Lie Theory

no. 1
Relationship between Nichols Braided Lie Algebras and Nichols algebras
Journal of Lie Theory, Volume 25 (2015) no. 1, pp. 45-63
We establish the relationship among Nichols algebras, Nichols braided Lie algebras and Nichols Lie algebras. We prove two results: (i) The Nichols algebra B(V) is finite-dimensional if and only if the Nichols braided Lie algebra L(V) is finite-dimensional if there does not exist any m-infinity element in B(V); (ii) the Nichols Lie algebra L-(V) is infinite dimensional if D- is infinite. We give sufficient conditions for the Nichols braided Lie algebra L(V) to be a homomorphic image of a braided Lie algebra generated by V with defining relations.
DOI: 10.5802/jolt.827
Classification: 16W30, 16G10
Keywords: Nichols Lie algebra, Nichols algebra, Nichols braided Lie algebra 
@article{JOLT_2015_25_1_a3,
     author = {W. Wu and S. Zhang and Y. Zhang},
     title = {Relationship between {Nichols} {Braided} {Lie} {Algebras} and {Nichols} algebras},
     journal = {Journal of Lie Theory},
     pages = {45--63},
     year = {2015},
     volume = {25},
     number = {1},
     doi = {10.5802/jolt.827},
     zbl = {1327.16019},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.827/}
}
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W. Wu; S. Zhang; Y. Zhang. Relationship between Nichols Braided Lie Algebras and Nichols algebras. Journal of Lie Theory, Volume 25 (2015) no. 1, pp. 45-63. doi: 10.5802/jolt.827

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