29 citations · 167 across the 26 of their papers we have counts for
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Principal fiber bundles in non-commutative geometry
Christian Kassel
These are the expanded notes of a course given at the Summer school "Geometric, topological and algebraic methods for quantum field theory" held at Villa de Leyva, Colombia in July…
The Noether problem for Hopf algebras
Christian Kassel, Akira Masuoka
In previous work, Eli Aljadeff and the first-named author attached an algebra B_H of rational fractions to each Hopf algebra H. The generalized Noether problem is the following: fo…
Generic base algebras and universal comodule algebras for some finite-dimensional Hopf algebras
Uma N. Iyer, Christian Kassel
After recalling the definitions and the properties of the generic base algebra and of the universal comodule algebra attached to a Hopf algebra by Aljadeff and the second-named aut…
Hopf algebras and polynomial identities
Christian Kassel
This is a survey of results obtained jointly with E. Aljadeff and published in Adv. Math. 218 (2008), 1453-1495. We explain how to set up a theory of polynomial identities for como…
Twisting algebras using non-commutative torsors
Pierre Guillot, Christian Kassel, Akira Masuoka
Non-commutative torsors (equivalently, two-cocycles) for a Hopf algebra can be used to twist comodule algebras. After surveying and extending the literature on the subject, we prov…
Flatness and freeness properties of the generic Hopf Galois extensions
Christian Kassel, Akira Masuoka
In previous work, to each Hopf algebra H and each invertible right two-cocycle on H, Eli Aljadeff and the first-named author attached a subalgebra B of the free commutative Hopf al…
Cohomology of invariant Drinfeld twists on group algebras
Pierre Guillot, Christian Kassel
We show how to compute a certain group of equivalence classes of invariant Drinfeld twists on the algebra of a finite group G over a field k of characteristic zero. This group is n…
Generic Hopf Galois extensions
Christian Kassel
In previous joint work with Eli Aljadeff we attached a generic Hopf Galois extension A(H,c) to each twisted algebra H(c) obtained from a Hopf algebra H by twisting its product with…
The lazy homology of a Hopf algebra
Julien Bichon, Christian Kassel
To any Hopf algebra H we associate two commutative Hopf algebras, which we call the first and second lazy homology Hopf algebras of H. These algebras are related to the lazy cohomo…
Polynomial identities and noncommutative versal torsors
Eli Aljadeff, Christian Kassel
To any cleft Hopf Galois object, i.e., any algebra H[t] obtained from a Hopf algebra H by twisting its multiplication with a two-cocycle t, we attach two "universal algebras" A(H,t…
Quantum principal bundles up to homotopy equivalence
Christian Kassel
We translate some fundamental properties satisfied by topological principal bundles into the setting of Hopf-Galois extensions. The properties are: functoriality, homotopy, and tri…
Homotopy theory of Hopf Galois extensions
Christian Kassel, Hans-Juergen Schneider
We introduce the concept of homotopy equivalence for Hopf Galois extensions and make a systematic study of it. As an application we determine all H-Galois extensions up to homotopy…
The Hall algebra of the category of coherent sheaves on the projective line
Pierre Baumann, Christian Kassel
To an abelian category A of homological dimension 1 satisfying certain finiteness conditions, one can associate an algebra, called the Hall algebra. Kapranov studied this algebra w…
Biquantization of Lie bialgebras
Christian Kassel, Vladimir Turaev
For any finite-dimensional Lie bialgebra , we construct a bialgebra over the ring , which quantizes simultaneously the universal enveloping bialgebra $U(…