Nichols algebras associated to the transpositions of the symmetric group are twist-equivalent

Abstract

Using the theory of covering groups of Schur we prove that the two Nichols algebras associated to the conjugacy class of transpositions in S_n are equivalent by twist and hence they have the same Hilbert series. These algebras appear in the classification of pointed Hopf algebras and in the study of quantum cohomology ring of flag manifolds.

Final version. 9 pages

References in corpus (3)

• Finite-dimensional pointed Hopf algebras with alternating groups are trivial
• Nichols algebras of group type with many quadratic relations
• Finite dimensional pointed Hopf algebras over S_4

Cited by in corpus (7)

• Twisted quantum Drinfeld Hecke algebras
• Multiparameter quantum groups, bosonizations and cocycle deformations
• On a family of Hopf algebras of dimension 72
• Three natural subgroups of the Brauer-Picard group of a Hopf algebra with applications
• On Hopf algebras whose coradical is a cocentral abelian cleft extension
• Twist equivalence for Nichols algebras over Coxeter groups
• Factorization of Graded Traces on Nichols Algebras