Geodesic
Relationship between Nichols Braided Lie Algebras and Nichols algebras
Weicai Wu1 ; Shouchuan Zhang1 ; Yao-Zhong Zhang2
1Department of Mathematics, Hunan University, Changsha 410082, P. R. China
2School of Mathematics and Physics, The University of Queensland, Brisbane 4072, Australia
Journal of Lie Theory, Tome 25 (2015) no. 1, pp. 45-63

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 16W30, 16G10
Mots-clés : Nichols Lie algebra, Nichols algebra, Nichols braided Lie algebra

Weicai Wu  1   ; Shouchuan Zhang  1   ; Yao-Zhong Zhang  2

1 Department of Mathematics, Hunan University, Changsha 410082, P. R. China
2 School of Mathematics and Physics, The University of Queensland, Brisbane 4072, Australia 
Weicai Wu; Shouchuan Zhang; Yao-Zhong Zhang. Relationship between Nichols Braided Lie Algebras and Nichols algebras. Journal of Lie Theory, Tome 25 (2015) no. 1, pp. 45-63. http://geodesic.mathdoc.fr/item/JOLT_2015_25_1_a3/
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     author = {Weicai Wu and Shouchuan Zhang and Yao-Zhong Zhang},
     title = {Relationship between {Nichols} {Braided} {Lie} {Algebras} and {Nichols} algebras},
     journal = {Journal of Lie Theory},
     pages = {45--63},
     year = {2015},
     volume = {25},
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