6 citations · 10 across the 8 of their papers we have counts for
9 papers
Lie algebras in symmetric tensor categories
Iván Angiono, Agustina Czenky, Pavel Etingof +3
We develop the general theory of Lie algebras in symmetric tensor categories. We prove categorical versions of classical results such as Engel's theorem, Cartan's criterion, and th…
Contragredient Lie algebras in symmetric categories
Iván Angiono, Julia Plavnik, Guillermo Sanmarco
We define contragredient Lie algebras in symmetric categories, generalizing the construction of Lie algebras of the form for a Cartan matrix from the category…
Semisimplification of contragredient Lie algebras
Iván Angiono, Julia Plavnik, Guillermo Sanmarco
We describe the structure and different features of Lie algebras in the Verlinde category, obtained as semisimplification of contragredient Lie algebras in characteristic with…
Finite-dimensional quantum groups of type Super A and non-semisimple modular categories
Robert Laugwitz, Guillermo Sanmarco
We construct a series of finite-dimensional quantum groups as braided Drinfeld doubles of Nichols algebras of type Super A, for an even root of unity, and classify ribbon structure…
Pointed Hopf algebras over non-abelian groups with non-simple standard braidings
Iván Angiono, Simon Lentner, Guillermo Sanmarco
We construct finite-dimensional Hopf algebras whose coradical is the group algebra of a central extension of an abelian group. They fall into families associated to a semisimple Li…
Finite GK-dimensional pre-Nichols algebras of (super)modular and unidentified type
Iván Angiono, Emiliano Campagnolo, Guillermo Sanmarco
We show that every finite GK-dimensional pre-Nichols algebra for braidings of diagonal type with connected diagram of modular, supermodular or unidentified type is a quotient of th…
Finite GK-Dimensional pre-Nichols algebras of super and standard type
Iván Angiono, Emiliano Campagnolo, Guillermo Sanmarco
We prove that finite GK-dimensional pre-Nichols algebras of super and standard type are quotients of the corresponding distinguished pre-Nichols algebras, except when the braiding…
Finite GK-dimensional pre-Nichols algebras of quantum linear spaces and of Cartan type
Nicolás Andruskiewitsch, Guillermo Sanmarco
We study pre-Nichols algebras of quantum linear spaces and of Cartan type with finite GK-dimension. We prove that out of a short list of exceptions involving only roots of order 2,…
Pointed Hopf algebras over non abelian groups with decomposable braidings, I
Iván Angiono, Guillermo Sanmarco
We describe all finite-dimensional pointed Hopf algebras whose infinitesimal braiding is a fixed Yetter-Drinfeld module decomposed as the sum of two simple objects: a point and the…