Normal Hopf Subalgebras in Cocycle Deformations of Finite Groups
نویسنده
چکیده
We determine necessary and sufficient conditions, in grouptheoretical terms, for a Hopf subalgebra in a cocycle deformation of a finite group to be normal.
منابع مشابه
Pointed and Copointed Hopf Algebras as Cocycle Deformations
We show that all finite dimensional pointed Hopf algebras with the same diagram in the classification scheme of Andruskiewitsch and Schneider are cocycle deformations of each other. This is done by giving first a suitable characterization of such Hopf algebras, which allows for the application of a result of Masuoka about Morita-Takeuchi equivalence and of Schauenburg about Hopf Galois extensio...
متن کاملCocycle Deformations for Hopf Algebras with a Coalgebra Projection
In this paper we study Hopf algebras with a coalgebra projection A ∼= R#ξH and their deformations by an H-bilinear cocycle. If γ is a cocycle for A, then γ can be restricted to a cocycle γR for R, and A γ ∼= RR#ξγH. As examples, we consider liftings of B(V )#K[Γ] where Γ is a finite abelian group, V is a quantum plane and B(V ) is its Nichols algebra, and explicitly construct the cocycle which ...
متن کاملCocycle Deformations and Brauer Group Isomorphisms
Let H be a Hopf algebra over a commutative ring k with unity and σ : H ⊗ H −→ k be a cocycle on H. In this paper, we show that the Yetter-Drinfeld module category of the cocycle deformation Hopf algebra H is equivalent to the Yetter-Drinfeld module category of H. As a result of the equivalence, the “quantum Brauer” group BQ(k,H) is isomorphic to BQ(k,H). Moreover, the group Gal(HR) constructed ...
متن کاملOn Group Theoretical Hopf Algebras and Exact Factorizations of Finite Groups
We show that a semisimple Hopf algebra A is group theoretical if and only if its Drinfeld double is a twisting of the Dijkgraaf-Pasquier-Roche quasi-Hopf algebra D(Σ), for some finite group Σ and some ω ∈ Z(Σ, k×). We show that semisimple Hopf algebras obtained as bicrossed products from an exact factorization of a finite group Σ are group theoretical. We also describe their Drinfeld double as ...
متن کاملDepth Two Hopf Subalgebras of Semisimple Hopf Algebras
Let H be a finite dimensional semisimple Hopf algebra over an algebraically closed field of characteristic zero. In this note we give a short proof of the fact that a Hopf subalgebra of H is a depth two subalgebra if and only if it is normal Hopf subalgebra.
متن کامل