
Journal of Lie Theory 25 (2015), No. 1, 045063 Copyright Heldermann Verlag 2015 Relationship between Nichols Braided Lie Algebras and Nichols algebras Weicai Wu Department of Mathematics, Hunan University, Changsha 410082, P. R. China weicaiwu@hnu.edu.cn Shouchuan Zhang Department of Mathematics, Hunan University, Changsha 410082, P. R. China sczhang@hnu.edu.cn YaoZhong Zhang School of Mathematics and Physics, The University of Queensland, Brisbane 4072, Australia yzz@maths.uq.edu.au 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 finitedimensional if and only if the Nichols braided Lie algebra L(V) is finitedimensional if there does not exist any minfinity 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. Keywords: Nichols Lie algebra, Nichols algebra, Nichols braided Lie algebra. MSC: 16W30, 16G10 [ Fulltextpdf (359 KB)] for subscribers only. 