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Finite-dimensional pointed Hopf algebras with alternating groups are trivial
(Springer Heidelberg, 2011-05)
It is shown that Nichols algebras over alternating groups Am (m ≥ 5) are infinite dimensional. This proves that any complex finite dimensional pointed Hopf algebra with group of group-likes isomorphic to Am is isomorphic ...
Copointed Hopf algebras over S4
(Elsevier Science, 2018-09)
We study the realizations of certain braided vector spaces of rack type as Yetter–Drinfeld modules over a cosemisimple Hopf algebra H. We apply the strategy developed in [1] to compute their liftings and use these results ...
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 ...
Algebras de Nichols de tipo diagonal /
(2011)
Esta tesis trata sobre la presentación de las álgebras de Nichols de tipo diagonal y su relación con las álgebras de Hopf punteadas. Usamos la definición de grupoide de Weyl y analizamos órdenes convexos para el sistema ...
On finite GK-dimensional Nichols algebra over abelian groups
(American Mathematical Society, 2021)
On finite GK-dimensional Nichols algebras of diagonal type
(American Mathematical Society, 2019-08)
We conjectured in a previous paper that a Nichols algebra of diagonal type with finite Gelfand-Kirillov dimension has finite (generalized) root system. We prove the conjecture assuming that the rank is 2. We also show that ...