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Drinfeld Codoubles of Hom–Hopf Algebras

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1 Published in 2019 at "Advances in Applied Clifford Algebras"

DOI: 10.1007/s00006-019-0949-0

Abstract: The main purpose of the present paper is to develop the theory of center constructions on Hom–Hopf algebras. Let H be a Hom–Hopf algebra, we first introduce the notions of nth Yetter–Drinfeld modules and mth… read more here.

Keywords: hom hopf; codoubles hom; algebras drinfeld; drinfeld codoubles ... See more keywords

Split Extensions and Actions of Bialgebras and Hopf Algebras

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1 Published in 2021 at "Applied Categorical Structures"

DOI: 10.1007/s10485-021-09659-5

Abstract: We introduce a notion of split extension of (non-associative) bialgebras. We show that this definition is equivalent to the notion of action of (non-associative) bialgebras. We particularize this equivalence to (non-associative) Hopf algebras by defining… read more here.

Keywords: associative hopf; extensions actions; non associative; hopf algebras ... See more keywords

Quasi-triangular Hopf algebras and invariant Jacobians

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0 Published in 2017 at "Science China Mathematics"

DOI: 10.1007/s11425-015-0867-x

Abstract: We show that two module homomorphisms for groups and Lie algebras established by Xi can be generalized to the setting of quasi-triangular Hopf algebras. These module homomorphisms played a key role in his proof of… read more here.

Keywords: quasi triangular; algebras invariant; hopf algebras; triangular hopf ... See more keywords

Hecke-Hopf algebras

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0 Published in 2019 at "Advances in Mathematics"

DOI: 10.1016/j.aim.2019.06.018

Abstract: 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… read more here.

Keywords: hopf algebras; hecke hopf; group;

Actions of cocommutative Hopf algebras

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0 Published in 2020 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2019.11.010

Abstract: Let $H$ be a cocommutative Hopf algebra acting on an algebra $A$. Assuming the base field to be algebraically closed and the $H$-action on $A$ to be integral, that is, it is given by a… read more here.

Keywords: actions cocommutative; hopf; algebra; cocommutative hopf ... See more keywords

Quantum differentials on cross product Hopf algebras

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1 Published in 2020 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2020.06.024

Abstract: We construct canonical strongly bicovariant differential graded algebra structures on all four flavours of cross product Hopf algebras, namely double cross products $A\hookrightarrow A\bowtie H\hookleftarrow H$, double cross coproducts $A\twoheadleftarrow A {\blacktriangleright\!\!\blacktriangleleft} H\twoheadrightarrow H$, biproducts… read more here.

Keywords: product hopf; quantum; hopf algebras; cross product ... See more keywords

Categorical aspects of cointegrals on quasi-Hopf algebras

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0 Published in 2020 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2020.08.012

Abstract: Abstract We discuss relations between some category-theoretical notions for a finite tensor category and cointegrals on a quasi-Hopf algebra. Specifically, for a finite-dimensional quasi-Hopf algebra H, we give an explicit description of categorical cointegrals of… read more here.

Keywords: quasi hopf; categorical aspects; category; cointegrals quasi ... See more keywords

A note on the discriminant of reflection Hopf algebras

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3 Published in 2022 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2022.04.009

Abstract: We provide a formula for commputing the discriminant of skew Calabi-Yau algebra over a central Calabi-Yau algebra. This method is applied to study the Jacobian and discriminant for reflection Hopf algebras. Introduction Recently, the discriminant… read more here.

Keywords: calabi yau; hopf; algebra; reflection ... See more keywords

Copointed Hopf algebras over S4

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1 Published in 2017 at "Journal of Pure and Applied Algebra"

DOI: 10.1016/j.jpaa.2017.10.020

Abstract: We study the realizations of certain braided vector spaces of rack type as Yetter-Drinfeld modules over a cosemisimple Hopf algebra H . We apply the strategy developed in [1] to compute their liftings and use… read more here.

Keywords: copointed hopf; hopf algebras;

One-sided Hopf algebras and quantum quasigroups

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0 Published in 2018 at "Communications in Algebra"

DOI: 10.1080/00927872.2018.1448847

Abstract: ABSTRACT We study the connections between one-sided Hopf algebras and one-sided quantum quasigroups, tracking the four possible invertibility conditions for the left and right composite morphisms that combine comultiplications and multiplications in these structures. The… read more here.

Keywords: one sided; sided hopf; hopf algebras; algebras quantum ... See more keywords

On Hopf algebras over the unique 12-dimensional Hopf algebra without the dual Chevalley property

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1 Published in 2019 at "Communications in Algebra"

DOI: 10.1080/00927872.2018.1508582

Abstract: Abstract Let be an algebraically closed field of characteristic zero. We determine all finite-dimensional Hopf algebras over whose Hopf coradical is isomorphic to the unique 12-dimensional Hopf algebra without the dual Chevalley property, such that… read more here.

Keywords: algebra without; hopf; unique dimensional; dimensional hopf ... See more keywords