Liftings of Nichols algebras of diagonal type III. Cartan type $G_2$

Agustín García Iglesias; João Matheus Jury Giraldi

doi:10.1016/j.jalgebra.2017.01.037

paper

Liftings of Nichols algebras of diagonal type III. Cartan type $G_{2}$

arXiv:1607.07857 · doi:10.1016/j.jalgebra.2017.01.037

Abstract

We complete the classification of Hopf algebras whose infinitesimal braiding is a principal Yetter-Drinfeld realization of a braided vector space of Cartan type $G_{2}$ over a cosemisimple Hopf algebra. We develop a general formula for a class of liftings in which the quantum Serre relations hold. We give a detailed explanation of the procedure for finding the relations, based on the recent work of Andruskiewitsch, Angiono and Rossi Bertone.

54 pages; including an appendix. Final version, to appear in J. Algebra

Liftings of Nichols algebras of diagonal type III. Cartan type G2​

Abstract

Liftings of Nichols algebras of diagonal type III. Cartan type $G_{2}$