68 citations · 183 across the 14 of their papers we have counts for
13 papers · 1 filter
On finite-dimensional copointed Hopf algebras over dihedral groups
Fernando Fantino, Gaston Andres Garcia, Mitja Mastnak
We classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero such that its coradical is isomorphic to the algebra of functions over a…
Conjugacy classes of p-cycles of type D in alternating groups
Fernando Fantino
We classify the conjugacy classes of p-cycles of type D in alternating groups. This finishes the open cases in arXiv:0812.4628. We also determine all the subracks of those conjugac…
On Nichols algebras associated to simple racks
N. Andruskiewitsch, F. Fantino, G. A. Garcia +1
This is a report on the present state of the problem of determining the dimension of the Nichols algebra associated to a rack and a cocycle. This is relevant for the classification…
The logbook of Pointed Hopf algebras over the sporadic groups
N. Andruskiewitsch, F. Fantino, M. Graña +1
In this notes we give details of the proofs performed with GAP of the theorems of our paper "Pointed Hopf Algebras over the Sporadic Simple Groups".
Pointed Hopf algebras over the sporadic simple groups
N. Andruskiewitsch, F. Fantino, M. Graña +1
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, t…
Pointed Hopf algebras over some sporadic simple groups
N. Andruskiewitsch, F. Fantino, M. Graña +1
Any finite-dimensional complex pointed Hopf algebra with group of group-likes isomorphic to a sporadic group, with the possible exception of the Fischer groups Fi22, the Baby Monst…
On pointed Hopf algebras associated with the symmetric groups II
N. Andruskiewitsch, F. Fantino, M. Graña +1
This is a sequel to arXiv:0807.2406. It is shown that the Nichols algebras over the symmetric groups S_m, m > 4, are all infinite-dimensional, except (maybe) those related to the t…
Finite-dimensional pointed Hopf algebras with alternating groups are trivial
N. Andruskiewitsch, F. Fantino, M. Graña +1
It is shown that Nichols algebras over alternating groups A_m, m>4, are infinite dimensional. This proves that any complex finite dimensional pointed Hopf algebra with group of gro…
On pointed Hopf algebras associated with the symmetric groups
Nicolás Andruskiewitsch, Fernando Fantino, Shouchuan Zhang
It is an important open problem whether the dimension of the Nichols algebra B(O,ρ) is finite when O is the class of the transpositions and ρis the sign representation, with m>= 6.…
New techniques for pointed Hopf algebras
N. Andruskiewitsch, F. Fantino
We present techniques that allow to decide that the dimension of some pointed Hopf algebras associated with non-abelian groups is infinite. These results are consequences of arXiv:…
On pointed Hopf algebras associated with the Mathieu simple groups
Fernando Fantino
Let G be a Mathieu simple group, s in G, O_s the conjugacy class of s and ρan irreducible representation of the centralizer of s. We prove that either the Nichols algebra B(O_s,ρ)…
On pointed Hopf algebras associated with alternating and dihedral groups
Nicolás Andruskiewitsch, Fernando Fantino
We classify finite-dimensional complex pointed Hopf algebra with group of group-like elements isomorphic to A_5. We show that any pointed Hopf algebra with infinitesimal braiding a…
On pointed Hopf algebras associated to unmixed conjugacy classes in S_n
Nicol'as Andruskiewitsch, Fernando Fantino
Let s in S_n be a product of disjoint cycles of the same length, C the conjugacy class of s and rho an irreducible representation of the isotropy group of s. We prove that either t…