Hopf quivers and Nichols algebras in positive characteristic

Claude Cibils (1) , Aaron Lauve (2) , Sarah Witherspoon (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 Department of Mathematics [Austin]

We apply a combinatorial formula of the first author and Rosso, for products in Hopf quiver algebras, to determine the structure of Nichols algebras. We illustrate this technique by explicitly constructing new examples of Nichols algebras in positive characteristic. We further describe the corresponding Radford biproducts and some liftings of these biproducts, which are new finite dimensional pointed Hopf algebras.

Mots clés: biproduct; pointed; Hopf; quivers; Nichols

Domaines: Algèbres quantiques [math.QA]

Claude Cibils, Aaron Lauve, Sarah Witherspoon. Hopf quivers and Nichols algebras in positive characteristic. Proceedings of the American Mathematical Society, 2009, 137, pp.4029-4041. ⟨10.1090/S0002-9939-09-10001-1⟩. ⟨hal-00356587v2⟩