Zhang, Xiaohui Guo, Shuangjian Wang, Shengxiang
Published in
Advances in Applied Clifford Algebras

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 Drinfeld codouble for H. Also we prove that the category YDHH(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepa...

Oesinghaus, Jakob
Published in
Research in the Mathematical Sciences

We show that the Hopf algebra of quasisymmetric functions arises naturally as the integral Chow ring of the algebraic stack of expanded pairs originally described by J. Li, using a more combinatorial description in terms of configurations of line bundles. In particular, we exhibit a gluing map which gives rise to the comultiplication. We then apply...

Chen, Jialei Yang, Shilin
Published in
Chinese Annals of Mathematics, Series B

Finite dimensional ribbon Hopf (super) algebras play an important role in constructing invariants of 3-manifolds. In the present paper, the authors give a necessary and sufficient condition for the Drinfel’d double of a finite dimensional Hopf superalgebra to have a ribbon element. The criterion can be seen as a generalization of Kauffman and Radfo...

Galindo, César Rowell, Eric Wang, Zhenghan
Published in
Quantum Information Processing

Acyclic anyon models are non-abelian anyon models for which thermal anyon errors can be corrected. In this note, we characterize acyclic anyon models and raise the question whether the restriction to acyclic anyon models is a deficiency of the current protocol or could it be intrinsically related to the computational power of non-abelian anyons. We...

Ma, Tianshui Li, Haiying Liu, Linlin
Published in
Chinese Annals of Mathematics, Series B

Let (H, β) be a Hom-bialgebra such that β2 = idH. (A, αA) is a Hom-bialgebra in the left-left Hom-Yetter-Drinfeld category HHYD and (B, αB) is a Hom-bialgebra in the right-right Hom-Yetter-Drinfeld category YDHH. The authors define the two-sided smash product Hom-algebra (A♮H♮B,αA⊗β⊗αB)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{...

Chen, Quanguo Wang, Dingguo Kang, Xiaodan
Published in
Frontiers of Mathematics in China

In this paper, the notion of a twisted partial Hopf coaction is introduced. The conditions on partial cocycles are established in order to construct partial crossed coproducts. Then the classification of partial crossed coproducts is discussed. Finally, some necessary and sufficient conditions for a class of partial crossed coproducts to be quasitr...

Cao, Haijun
Published in
Frontiers of Mathematics in China

We define the right regular dual of an object X in a monoidal category C; and give several results regarding the weak rigid monoidal category. Based on the definition of the right regular dual, we construct a weak Hopf algebra structure of H = End(F) whenever (F; J) is a fiber functor from category C to Vec and every X ∈ C has a right regular dual....

Andruskiewitsch, Nicolás García Iglesias, Agustín
Published in
ANNALI DELL'UNIVERSITA' DI FERRARA

Let H be a Hopf algebra. Any finite-dimensional lifting of V∈HHYD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V\in {}^{H}_{H}\mathcal {YD}$$\end{document} arising as...

Yang, Tao Zhou, Xuan Chen, Juzhen
Published in
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

Based on a pairing of two regular multiplier Hopf algebras A and B, Heisenberg double H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathscr {H}$$\end{document} is t...

Balan, Adriana
Published in
Applied Categorical Structures

Let U be a strong monoidal functor between monoidal categories. If it has both a left adjoint L and a right adjoint R, we show that the pair (R,L) is a linearly distributive functor and (U,U)⊣(R,L) is a linearly distributive adjunction, if and only if L⊣U is a Hopf adjunction and U⊣R is a coHopf adjunction. We give sufficient conditions for a stron...