Lecture notes on Nichols algebras

Overview & Synopsis

This note contains below topics, Preliminaries on Lie algebras, Preliminaries on braided tensor categories, Preliminaries on quantum groups, Nichols algebras, Nichols algebras via quantum symmetrizer, Categorical algebras, Quantum symmetrizer, First examples, Nichols algebras as universal Hopf algebras, Categorical Hopf algebras, Root systems, Root system from Nichols algebras, Axiomatization of generalized root systems, Hyperplane arrangements, Cartan graph and Weyl groupoid, Classification in Rank 2.