Related papers: Hopf actions on filtered regular algebras
We consider finite-dimensional Hopf algebras $u$ which admit a smooth deformation $U\to u$ by a Noetherian Hopf algebra $U$ of finite global dimension. Examples of such Hopf algebras include small quantum groups over the complex numbers,…
We construct explicit Drinfel'd twists for the generalized Cartan type $H$ Lie algebras in characteristic $0$ and obtain the corresponding quantizations and their integral forms. Via making modular reductions including modulo $p$ reduction…
In this work we study how to extend a partial action of a Hopf Algebra $A$ on an algebra $R$ to a partial action of a Hopf-Ore extension of $A$ on $R$. As consequence, we characterize all partial actions of rank one Hopf algebras (in…
We describe all possible coactions of finite groups (equivalently, all group gradings) on two-dimensional Artin-Schelter regular algebras. We give necessary and sufficient conditions for the associated Auslander map to be an isomorphism,…
This is a contribution to the classification of finite-dimensional Hopf algebras over an algebraically closed field $\Bbbk$ of characteristic 0. Concretely, we show that a finite-dimensional Hopf algebra whose Hopf coradical is basic is a…
A class of finite-dimensional Hopf algebras which generalise the notion of Taft algebras is studied. We give necessary and sufficient conditions for these Hopf algebras to omit a pair in involution, that is, to not have a group-like and a…
Family of doublings of Hopf algeras based on the product of algebra and its dual are constructed and studied. Special cases of these construction may be considered as natural quantum analogs of rings of differential operators on groups.…
We classify finite-dimensional Nichols algebras of Yetter-Drinfeld modules with indecomposable support over finite solvable groups in characteristic 0, using a variety of methods including reduction to positive characteristic. As a…
By means of the notions of cross product algebras of the theory of quantum groups, in the context of classical Hopf algebra structures, we deduce some known structures of Weyl algebras type (as the Drinfeld quantum double, the restricted…
The objects of study in this paper are Hopf algebras $H$ which are finitely generated algebras over an algebraically closed field and are extensions of a commutative Hopf algebra by a finite dimensional Hopf algebra. Basic structural and…
We develop a notion of formal groups in the filtered setting and describe a duality relating these to a specified class of filtered Hopf algebras. We then study a deformation to the normal cone construction in the setting of derived…
Connes and Kreimer have discovered a Hopf algebra structure behind renormalization of Feynman integrals. We generalize the Hopf algebra to the case of ribbon graphs, i.e. to the case of theories with matrix fields. The Hopf algebra is…
Partial actions of Hopf algebras can be considered as a generalization of partial actions of groups on algebras. Among important properties of partial Hopf actions, it is possible to prove the existence of enveloping actions, i.e., every…
Let $H$ be a finite-dimensional connected Hopf algebra over an algebraically closed field $\field$ of characteristic $p>0$. We provide the algebra structure of the associated graded Hopf algebra $\gr H$. Then, we study the case when $H$ is…
In this paper, we construct the Grothendieck ring of a class of 2$n^2$-dimension semisimple Hopf Algebras $H_{2n^2}$, which can be viewed as a generalization of the 8-dimension Kac-Paljutkin Hopf algebra $K_8$. All irreducible…
Under the assumption that a residually finite dimensional Hopf algebra H has an Artinian ring of fractions it is proved that H is a flat module over any right coideal subalgebra satisfying a polynomial identity and is faithfully flat over…
We consider graded deformations and PBW deformations of algebras defined over noncommutative algebras. We explain how fibers of graded deformations correspond to filtered algebras admitting a PBW property, with focus on smash product…
Let R be a polynomial ring in r variables and D a dual ring upon which R acts as partial differential operators (classical apolarity). For a type two graded level Artinian algebras A=R/I, of socle degree j we consider the family of Artinian…
A method is suggested for obtaining the Plancherel measure for Affine Hecke Algebras as a limit of integral-type formulas for inner products in the polynomial and related modules of Double Affine Hecke Algebras. The analytic continuation…
In this work, we review some properties of twisted partial actions of Hopf algebras on unital algebras and give necessary and sufficient conditions for a twisted partial action to have a globalization. We also elaborate a series of…