ﻻ يوجد ملخص باللغة العربية
The notions of Galois and cleft extensions are generalized for coquasi-Hopf algebras. It is shown that such an extension over a coquasi-Hopf algebra is cleft if and only if it is Galois and has the normal basis property. A Schneider type theorem is proven for coquasi-Hopf algebras with bijective antipode. As an application, we generalize Schauenburgs bialgebroid construction for coquasi-Hopf algebras.
The notion of crossed product by a coquasi-bialgebra H is introduced and studied. The resulting crossed product is an algebra in the monoidal category of right H-comodules. We give an interpretation of the crossed product as an action of a monoidal c
If H is a finite dimensional quasi-Hopf algebra and A is a left H-module algebra, we prove that there is a Morita context connecting the smash product A#H and the subalgebra of invariants A^{H}. We define also Galois extensions and prove the connection with this Morita context, as in the Hopf case.
In this work we deal with partial (co)action of multiplier Hopf algebras on not necessarily unital algebras. Our main goal is to construct a Morita context relating the coinvariant algebra $R^{underline{coA}}$ with a certain subalgebra of the smash p
Let $p$ and $q$ be distinct prime numbers. We study the Galois objects and cocycle deformations of the noncommutative, noncocommutative, semisimple Hopf algebras of odd dimension $p^3$ and of dimension $pq^2$. We obtain that the $p+1$ non-isomorphic
Let $W$ be a Coxeter group. The goal of the paper is to construct new Hopf algebras that contain Hecke algebras $H_{bf q}(W)$ as (left) coideal subalgebras. Our Hecke-Hopf algebras ${bf H}(W)$ have a number of applications. In particular they provide