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Liftings of Nichols algebras of diagonal type I. cartan type A
(Oxford University Press, 2017-05)
After the classification of the finite-dimensional Nichols algebras of diagonal type[17,18], the determination of its defining relations[7,6], and the verification of the generation in degree-s1 conjecture[6], there is ...
On the Hopf algebra structure of the lusztig quantum divided power algebrasSur la structure d’algèbre de Hopf des algèbres de puissances divisées quantiques de lusztig
(Universite Clermont Auvergne, 2020-03-09)
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 enveloping algebra of an abelian Lie algebra. ...
On twisted conjugacy classes of type D in sporadic simple groups
(American Mathematical Society, 2013-02)
We determine twisted conjugacy classes of type D associated with the sporadic simple groups. This is an important step in the program of the classification of finite-dimensional pointed Hopf algebras with non-abelian ...
On rigidity of Nichols algebras
(Elsevier Science, 2015-12)
We study deformations of graded braided bialgebras using cohomological methods. In particular, we show that many examples of Nichols algebras, including the finite-dimensional ones arising in the Andruskiewitsch-Schneider ...
Pointed Hopf algebras over non abelian groups with decomposable braidings, I
(Academic Press Inc Elsevier Science, 2020-05)
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 one of transpositions of the symmetric ...
Pointed Hopf algebras over the sporadic simple groups
(Academic Press Inc Elsevier Science, 2011-01)
We show that every finite-dimensional complex pointed Hopf algebra with group of group-likes isomorphic to a sporadic group is a group algebra, except for the Fischer group Fi22, the Baby Monster and the Monster. For these ...
On the representation theory of the Drinfeld Double of the Fomin-Kirillov Algebra FK 3
(Springer, 2018-09-13)
Let D be the Drinfeld double of FK3#S3 . We have described the simple D-modules in Pogorelsky and Vay (Adv. Math. 301, 423-457, 2016). In the present work, we describe the indecomposable summands of the tensor products ...
Verma and simple modules for quantum groups at non-abelian groups
(Academic Press Inc Elsevier Science, 2016-10)
The Drinfeld double D of the bosonization of a finite-dimensional Nichols algebra B(V) over a finite non-abelian group G is called a quantum group at a non-abelian group. We introduce Verma modules over such a quantum group ...
Bruhat order and nil-Hecke algebras for Weyl groupoids
(World Scientific, 2018-09)
We introduce nil-Hecke algebras for Weyl groupoids. We describe a basis and some properties of these algebras which lead to a notion of Bruhat order for Weyl groupoids.
The quantum divided power algebra of a finite-dimensional Nichols algebra of diagonal type
(International Press Boston, 2017-01)
Let Bq be a finite-dimensional Nichols algebra of diagonal type corresponding to a matrix q. We consider the graded dual Lq of the distinguished pre-Nichols algebra Bq from [A3] and the quantum divided power algebra Uq, a ...