Some remarks on Nichols algebras

Abstract

Two algebras can be attached to a braided vector space $(V, c)$ in an intrinsic way; the FRT-bialgebra and the Nichols algebra $\toba(V, c)$. The FRT-bialgebra plays the r\^ole of the algebra of quantum matrices, whereas the r\^ole of the Nichols algebra is less understood. Some authors call $\toba(V)$ a quantum symmetric algebra. The purpose of this paper is to discuss some properties of certain Nichols algebras, in an attempt to establish classes of Nichols algebras which are worth of further study.