590 citations
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9 papers · 1 filter
Classifying Hopf algebras of a given dimension
Margaret Beattie, Gaston Andres Garcia
Classifying all Hopf algebras of a given finite dimension over the complex numbers is a challenging problem which remains open even for many small dimensions, not least because few…
Techniques for classifying Hopf algebras and applications to dimension p^3
Margaret Beattie, Gaston Andres Garcia
The classification of all Hopf algebras of a given finite dimension over an algebraically closed field of characteristic 0 is a difficult problem. If the dimension is a prime, then…
Cocycle deformations for liftings of quantum linear spaces
Alessandro Ardizzoni, Margaret Beattie, Claudia Menini
Let be a Hopf algebra over a field of characteristic 0 and suppose there is a coalgebra projection from to a sub-Hopf algebra that splits the inclusion. If the…
Cocycle deformations for Hopf algebras with a coalgebra projection
Alessandro Ardizzoni, Margaret Beattie, Claudia Menini
Let be a Hopf algebra over a field of characteristic and let be a bialgebra or Hopf algebra such that is isomorphic to a sub-Hopf algebra of and there is an…
The antipode of a dual quasi-Hopf algebra with nonzero integrals is bijective
Margaret Beattie, Miodrag Cristian Iovanov, Serban Raianu
For a Hopf algebra of arbitrary dimension over a field , it is well-known that if has nonzero integrals, or, in other words, if the coalgebra is co-Frobenius, then t…
On the antipode of a co-Frobenius (co)quasitriangular Hopf algebra
Margaret Beattie, Daniel Bulacu
We extend to the co-Frobenius case a result of Drinfeld and Radford related to the fourth power of the antipode of a finite dimensional (co)quasitriangular Hopf algebra.