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Liftings of Nichols algebras of diagonal type III. Cartan type $G_2$ (1607.07857v3)
Published 26 Jul 2016 in math.QA
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.