arXiv subjects
Publications and source records attributed to João Matheus Jury Giraldi.
We determine some Nichols algebras that admit a non-trivial quadratic relation associated to some families of upper triangular solutions of the Yang-Baxter equation of dimension 3.
We compute all Nichols algebras of rigid vector spaces of dimension 2 that admit a non-trivial quadratic relation.
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.