68 citations · 415 across the 85 of their papers we have counts for
89 papers · 1 filter
On the Drinfeld doubles of Laistrygonian algebras in positive characteristic
Nicolás Andruskiewitsch, Dirceu Bagio, Saradia Della Flora +3
In this work, we study restricted Laistrygonian algebras over a field of positive characteristic . We compute their Drinfeld double and give explicit present…
Higher Fomin-Kirillov algebras are infinite-dimensional
N. Andruskiewitsch, I. Angiono, I. Heckenberger +3
We show that the Fomin--Kirillov algebras are infinite-dimensional for . This answers a question posed by Fomin and Kirillov in 1997. To prove this, we demonstrate t…
Hopf algebras over Chevalley groups
Nicolás Andruskiewitsch, Giovanna Carnovale
We show that every finite-dimensional pointed Hopf algebra over a finite simple Chevalley group, different from with q= 3 mod 4 (and from ), is…
On the finite generation of the cohomology of bosonizations
Nicolás Andruskiewitsch, David Jaklitsch, Van C. Nguyen +4
We use deformation sequences of (Hopf) algebras, extending the results of Negron and Pevtsova, to show that bosonizations of some suitable braided Hopf algebras by some suitable fi…
Pointed Hopf algebras of odd dimension and Nichols algebras over solvable groups
N. Andruskiewitsch, I. Heckenberger, L. Vendramin
We classify finite-dimensional Nichols algebras of Yetter-Drinfeld modules with indecomposable support over finite solvable groups in characteristic 0, using a variety of methods i…
On the finite generation of the cohomology of abelian extensions of Hopf algebras
Nicolás Andruskiewitsch, Sonia Natale
A finite-dimensional Hopf algebra is called quasi-split if it is Morita equivalent to a split abelian extension of Hopf algebras. Combining results of Schauenburg and Negron, it is…
On the bosonization of the enveloping algebra of a finite dimensional Lie superalgebra
Nicolás Andruskiewitsch, Ken A. Brown
We exhibit a PI Hopf algebra that is not a finite module over its center. We survey some ring-theoretical properties of the bosonizations of enveloping algebras of Lie superalgebra…
On infinite-dimensional Hopf algebras
Nicolás Andruskiewitsch
This is a survey on pointed Hopf algebras with finite Gelfand-Kirillov dimension and related aspects of the theory of infinite-dimensional Hopf algebras.
A class of finite-by-cocommutative Hopf algebras
Nicolás Andruskiewitsch, Sonia Natale, Blas Torrecillas
We present a rich source of Hopf algebras starting from a cofinite central extension of a Noetherian Hopf algebra and a subgroup of the algebraic group of characters of the central…
On the Drinfeld double of the restricted Jordan plane in characteristic
Nicolás Andruskiewitsch, Dirceu Bagio, Saradia Della Flora +1
We consider the restricted Jordan plane in characteristic , a finite-dimensional Nichols algebra quotient of the Jordan plane that was introduced by Cibils, Lauve and Witherspoo…
Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type VII. Semisimple classes in PSL(n,q) and PSp(2n,q)
N. Andruskiewitsch, G. Carnovale, G. García
We show that the Nichols algebra of a simple Yetter-Drinfeld module over a projective special linear group over a finite field whose support is a semisimple orbit has infinite dime…
Corrigendum: Liftings of the Jordan plane
Nicolás Andruskiewitsch, Iván Angiono, István Heckenberger
We complete the classification of the pointed Hopf algebras with finite Gelfand-Kirillov dimension that are liftings of the Jordan plane over a nilpotent-by-finite group, correctin…
On the Laistrygonian Nichols algebras that are domains
Nicolás Andruskiewitsch, Dirceu Bagio, Saradia Della Flora +1
We consider a class of Nichols algebras introduced in [3] which are domains and have many favorable properties like AS-regular and st…
Rank 4 Nichols Algebras of Pale Braidings
Nicolás Andruskiewitsch, Iván Angiono, Matías Moya Giusti
We classify finite GK-dimensional Nichols algebras of rank 4 such that arises as a Yetter-Drinfeld module over an abelian group but it is not a direct sum of…
On finite GK-dimensional Nichols algebras of diagonal type: rank 3 and Cartan type
Iván Angiono, Agustín García Iglesias
This paper contributes to the proof of the conjecture posed in arXiv:1606.02521, stating that a Nichols algebra of diagonal type with finite Gelfand-Kirillov dimension has finite (…
On pointed Hopf algebras over nilpotent groups
Nicolás Andruskiewitsch
We classify finite-dimensional Nichols algebras over finite nilpotent groups of odd order in group-theoretical terms. The main step is to show that the conjugacy classes of such fi…
On the double of the (restricted) super Jordan plane
Nicolás Andruskiewitsch, Héctor Peña Pollastri
We consider the super Jordan plane, a braided Hopf algebra introduced--to the best of our knowledge--in works of N. Andruskiewitsch, I. Angiono, I. Heckenberger, and its restricted…
Poisson orders on large quantum groups
Nicolás Andruskiewitsch, Iván Angiono, Milen Yakimov
We develop a Poisson geometric framework for studying the representation theory of all contragredient quantum super groups at roots of unity. This is done in a uniform fashion by t…
On the Hopf algebra structure of the Lusztig quantum divided power algebras
Nicolás Andruskiewitsch, Iván Angiono, Cristian Vay
We study the Hopf algebra structure of Lusztig's quantum groups. First we show that the zero part is the tensor product of the group algebra of a finite abelian group with the enve…
Examples of finite-dimensional pointed Hopf algebras in characteristic
Nicolás Andruskiewitsch, Dirceu Bagio, Saradia Della Flora +1
We present new examples of finite-dimensional Nichols algebra over fields of characteristic 2 starting from braided vector spaces that are not of diagonal type, admit realizations…
Cohomology rings of finite-dimensional pointed Hopf algebras over abelian groups
Nicolás Andruskiewitsch, Iván Angiono, Julia Pevtsova +1
We show that the cohomology ring of a finite-dimensional complex pointed Hopf algebra with an abelian group of group-like elements is finitely generated. Our strategy has three maj…
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,…
On the restricted Jordan plane in odd characteristic
Nicolás Andruskiewitsch, Héctor Peña Pollastri
In positive characteristic the Jordan plane covers a finite-dimensional Nichols algebra that was described by Cibils, Lauve and Witherspoon and we call the restricted Jordan plane.…
Lie algebras arising from Nichols algebras of diagonal type
Nicolás Andruskiewitsch, Iván Angiono, Fiorela Rossi Bertone
Let be a finite-dimensional Nichols algebra of diagonal type with braiding matrix , let be the correspondin…