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Álgebras de Nichols sobre grupos diedrales y pecios kthulhu en grupos esporádicos
(2020)
Esta tesis presenta aportes al problema de la clasificación de las álgebras de Hopf punteadas de dimensión finita sobre grupos no abelianos en el contexto del método del levante de N. Anduskiewitsch y H.-J. Schneider. El ...
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 ...
On finite dimensional Nichols algebras of diagonal type
(SpringerOpen, 2017-12)
This is a survey on Nichols algebras of diagonal type with finite dimension, or more generally with arithmetic root system. The knowledge of these algebras is the cornerstone of the classification program of pointed Hopf ...
Nichols algebras over groups with finite root system of rank two III
(Academic Press Inc Elsevier Science, 2015-01)
We compute the finite-dimensional Nichols algebras over the sum of two simple Yetter-Drinfeld modules V and W over non-abelian epimorphic images of a certain central extension of the dihedral group of eight elements or ...
Examples of pointed color Hopf algebras
(2014)
We present examples of color Hopf algebras, i.e. Hopf algebras in color categories (braided tensor categories with braiding induced by a bicharacter on an abelian group), related with quantum doubles of pointed Hopf algebras. ...
Examples of pointed color Hopf algebras
(World Scientific, 2014-04)
We present examples of color Hopf algebras, i.e. Hopf algebras in color categories (braided tensor categories with braiding induced by a bicharacter on an abelian group), related with quantum doubles of pointed Hopf algebras. ...
Finite-dimensional Nichols algebras over dual Radford algebras
(World Scientific, 2021-01)
For n, m ∈ N, let Hn,m be the dual of the Radford algebra of dimension n 2m. We present new finite-dimensional Nichols algebras arising from the study of simple Yetter-Drinfeld modules over Hn,m. Along the way, we describe ...
A finite-dimensional Lie algebra arising from a Nichols algebra of diagonal type (rank 2)
(Belgian Mathematical Soc Triomphe, 2017-01)
Let Bq be a finite-dimensional Nichols algebra of diagonal type corresponding to a matrix q ∈ k θ×θ . Let Lq be the Lusztig algebra associated to Bq [AAR]. We present Lq as an extension (as braided Hopf algebras) of Bq by ...
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 ...