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 rôle of the algebra of quantum matrices, whereas the rôle 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.

Cited by in corpus (6)

• Pointed Hopf algebras over the sporadic simple groups
• The Nichols algebra of screenings
• Logarithmic ^sl(2) CFT models from Nichols algebras. 1
• Finite dimensional rank 2 Nichols algebras of diagonal type I: Examples
• Fusion in the entwined category of Yetter--Drinfeld modules of a rank-1 Nichols algebra
• A note on the "logarithmic-W_3" octuplet algebra and its Nichols algebra