Relationship between Nichols braided Lie algebras and Nichols algebras

Abstract

We establish the relationship among Nichols algebras, Nichols braided Lie algebras and Nichols Lie algebras. We prove two results: (i) Nichols algebra $\mathfrak{B}(V)$ is finite-dimensional if and only if Nichols braided Lie algebra $\mathfrak{L}(V)$ is finite-dimensional if there does not exist any $m$-infinity element in $\mathfrak{B}(V)$; (ii) Nichols Lie algebra ${\mathfrak{L}}^{-}(V)$ is infinite dimensional if $D^{-}$ is infinite. We give the sufficient conditions for Nichols braided Lie algebra $\mathfrak{L}(V)$ to be a homomorphic image of a braided Lie algebra generated by $V$ with defining relations.

LeTex 18 pages, need JOLT-macros to compile. To appear in Journal of Lie Theory

References in corpus (2)

• A Milnor-Moore Type Theorem for Primitively Generated Braided Bialgebras
• Nichols algebras of unidentified diagonal type