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Representations of copointed Hopf algebras arising from the tetrahedron rack
(Springer, 2013-12)
We study the copointed Hopf algebras attached to the Nichols algebra of the affine rack Aff(F4,w), also known as tetrahedron rack, and the 2-cocycle −1. We investigate the so-called Verma modules and classify all the ...
De-Equivariantization of Hopf Algebras
(Springer, 2014-02)
We study the de-equivariantization of a Hopf algebra by an affine group scheme and we apply Tannakian techniques in order to realize it as the tensor category of comodules over a coquasi-bialgebra. As an application we ...
Álgebras de Hopf fracas associadas a grupóides duplos vacantes
(Universidade Federal de Santa MariaBrasilMatemáticaUFSMPrograma de Pós-Graduação em MatemáticaCentro de Ciências Naturais e Exatas, 2015-08-28)
Não foi possível inserir o abstract.
On Hopf algebras with triangular decomposition
(AMS, 2019-04)
In this survey, we first review some known results on the representationtheory of algebras with triangular decomposition, including the classification of the simple modules. We then discuss a recipe to construct Hopf ...
Minimum depth of double cross product extensions
(2020)
In this paper we explore minimum odd and minimum even depth sub- algebra pairs in the context of double cross products of finite dimensional Hopf algebras. We start by defining factorization algebras and outline how subring ...
Families of finite-dimensional Hopf algebras with the Chevalley property
(Springer, 2013-10)
We introduce and study new families of nite-dimensional Hopf algebras with the Chevalley property that are not pointed nor semisimple arising as twistings of quantum linear spaces. These Hopf algebras generalize the examples ...
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 ...
Invertible bimodule categories over the representation category of a Hopf algebra
(2014-02-12)
For any finite-dimensional Hopf algebra H we construct a group homomorphism
BiGal (H) → BrPic(Rep(H)), from the group of equivalence classes of H-biGalois
objects to the group of equivalence classes of invertible exact ...
PBW deformations of a Fomin–Kirillov Algebra and other examples
(Springer, 2018-09-26)
We begin the study of PBW deformations of graded algebras relevant to the theory of Hopf algebras. One of our examples is the Fomin–Kirillov algebra E3. Another one appeared in a paper of García Iglesias and Vay. As a ...