24 citations · 43 across the 13 of their papers we have counts for
17 papers · 1 filter
Irreducible representations of pointed Hopf algebras of type
Agustín García Iglesias, Alfio Antonio Rodriguez
We classify the irreducible representations of a family of finite-dimensional pointed liftings of the Nichols algebra associated with the diagram with parameter .…
On the representations of a family of pointed Hopf algebras
Agustin Garcia Iglesias, Alfio Antonio Rodriguez
For each and , we study the representations of a family of pointed Hopf algebras . These arise as Hopf cocycle deformations of the grad…
Finite GK-dimensional Nichols algebras of diagonal type and finite root systems
Iván Angiono, Agustín García Iglesias
Let be a finite-dimensional braided vector space of diagonal type. We show that the Gelfand Kirillov dimension of the Nichols algebra is finite if and onl…
Examples of liftings of modular and unidentified type: ufo(7,8) and br(2,a)
Agustín García Iglesias, Edwin Pacheco Rodríguez
We compute all liftings of braidings of unidentified types ufo(7) and ufo(8). Some of these examples had been previously computed by Helbig. We also present a list of examples of l…
Hopf-Galois structures on ambiskew polynomial rings
Julien Bichon, Agustín García Iglesias
We provide necessary and sufficient conditions to extend the Hopf-Galois algebra structure on an algebra R to a generalized ambiskew ring based on R, in a way such that the added v…
Pointed Hopf algebras: a guided tour to the liftings
Iván Angiono, Agustín García Iglesias
This article serves a two-fold purpose. On the one hand, it is a survey about the classification of finite-dimensional pointed Hopf algebras with abelian coradical, whose final ste…
Copointed Hopf algebras over
Agustín García Iglesias, Cristian Vay
We study the realizations of certain braided vector spaces of rack type as Yetter-Drinfeld modules over a cosemisimple Hopf algebra . We apply the strategy developed in arXiv:12…
Liftings of Nichols algebras of diagonal type III. Cartan type
Agustín García Iglesias, João Matheus Jury Giraldi
We complete the classification of Hopf algebras whose infinitesimal braiding is a principal Yetter-Drinfeld realization of a braided vector space of Cartan type over a cosemi…
Liftings of Nichols algebras of diagonal type I. Cartan type A
Nicolás Andruskiewitsch, Iván Angiono, Agustín García Iglesias
After the classification of the finite-dimensional Nichols algebras of diagonal type arXiv:math/0411477, arXiv:math/0605795, the determination of its defining relations arXiv:1008.…
-semisimple twisted conjugacy classes of type D in
Giovanna Carnovale, Agustín García Iglesias
Let be an odd prime, and set , . Let be a standard graph automorphism of , be a diagonal automorphism and $\oper…
Lifting via cocycle deformation
Nicolás Andruskiewitsch, Iván Angiono, Agustín García Iglesias +2
We develop a strategy to compute all liftings of a Nichols algebra over a finite dimensional cosemisimple Hopf algebra. We produce them as cocycle deformations of the bosonization…
Finite-dimensional Pointed or Copointed Hopf algebras over affine racks
Agustín García Iglesias, Cristian Vay
We study the pointed or copointed liftings of Nichols algebras associated to affine racks and constant cocycles for any finite group admitting a principal YD-realization of these r…
From Hopf algebras to tensor categories
Nicolas Andruskiewitsch, Ivan Angiono, Agustin Garcia Iglesias +2
This is a survey on spherical Hopf algebras. We give criteria to decide when a Hopf algebra is spherical and collect examples. We discuss tilting modules as a mean to obtain a fusi…
Representations of the category of modules over pointed Hopf algebras over S_3 and S_4
Agustín García Iglesias, Martín Mombelli
We classify exact indecomposable module categories over the representation category of all non-trivial Hopf algebras with coradical S_3 and S_4. As a byproduct, we compute all its…
Pointed Hopf algebras with standard braiding are generated in degree one
Iván Angiono, Agustín García Iglesias
We show that any finite-dimensional pointed Hopf algebra over an abelian group such that its infinitesimal braiding is of standard type is generated by group-like and skew-prim…
Representations of pointed Hopf algebras over S_3
Agustin Garcia Iglesias
The classification of finite-dimensional pointed Hopf algebras with group S_3 was finished in "The Nichols algebra of a semisimple Yetter-Drinfeld module", arXiv:0803.2430v1 [math.…
Finite dimensional pointed Hopf algebras over S_4
Gaston Andres Garcia, Agustin Garcia Iglesias
Let k be an algebraically closed field of characteristic 0. We conclude the classification of finite dimensional pointed Hopf algebras whose group of group-likes is S_4. We also de…