Esta tesis trata sobre la clasificación de las álgebras de pre-Nichols de dimensión de Gelfand-Kirillov finita. Las álgebras de Nichols de tipo diagonal de dimensión finita con diagrama de Dynkin conexo se pueden reagrupar ...

This is a contribution to the classification of finite-dimensional Hopf algebras over an algebraically closed field k of characteristic 0. Concretely, we show that a finite-dimensional Hopf algebra whose Hopf coradical is ...

Esta tesis es un aporte a la clasificación de las álgebras de Hopf punteadas de dimensión de Gelfand-Kirillov finita sobre cuerpos algebraicamente cerrados y de característica cero. En una primera instancia nos concentramos ...

We give an explicit and essentially minimal list of defining relations of a Nichols algebra of diagonal type with finite root system. This list contains the well-known quantum Serre relations but also many new variations. ...

Nichols algebras, Hopf algebras in braided categories with distinguishedproperties, were discovered several times. They appeared for the first time in the thesis of W. Nichols [72], aimed to construct new examples of Hopf ...

We describe how to find quantum determinants and antipode formulas from braidedvector spaces using the FRT-construction and finite-dimensional Nichols algebras. It improvesthe construction of quantum function algebras using ...

We compute all Nichols algebras of rigid braided vector spaces of dimension 2 that admit a non-trivial quadratic relation.

We obtain a presentation by generators and relations of any Nichols algebra of diagonal type with finite root system. We prove that the defining ideal is finitely generated. The proof is based on Kharchenko's theory of PBW ...