On pointed Hopf algebras associated with the symmetric groups

Abstract

It is an important open problem whether the dimension of the Nichols algebra B(O,ρ) is finite when O is the class of the transpositions and ρis the sign representation, with m>= 6. In the present paper, we discard most of the other conjugacy classes showing that very few pairs (O,ρ) might give rise to finite-dimensional Nichols algebras.

14 pages; typos added in abstract

References in corpus (2)

• Finite-dimensional pointed Hopf algebras with alternating groups are trivial
• Root systems and Weyl groupoids for Nichols algebras

Cited by in corpus (4)

• Right coideal subalgebras of Nichols algebras and the Duflo order on the Weyl groupoid
• On Pointed Hopf Algebras with Weyl Groups of exceptional type
• The radicals of (Braided) Lie algebras
• On Pointed Hopf Algebras with Sporadic Simple Groups $\mathrm{HS}$ and $Co3$