Displaying similar documents to “Bicovariant differential calculi and cross products on braided Hopf algebras”

Smash (co)products and skew pairings.

José N. Alonso Alvarez, José Manuel Fernández Vilaboa, Ramón González Rodríguez (2001)

Publicacions Matemàtiques

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Let τ be an invertible skew pairing on (B,H) where B and H are Hopf algebras in a symmetric monoidal category C with (co)equalizers. Assume that H is quasitriangular. Then we obtain a new algebra structure such that B is a Hopf algebra in the braided category γD and there exists a Hopf algebra isomorphism w: B ∞ H → B [×] H in C, where B ∞ H is a Hopf algebra with (co)algebra structure the smash (co)product and B [×] H is the Hopf algebra defined by Doi and Takeuchi. ...

Representations, duals and quantum doubles of monoidal categories

Majid, Shahn

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[For the entire collection see Zbl 0742.00067.]The Tanaka-Krein type equivalence between Hopf algebras and functored monoidal categories provides the heuristic strategy of this paper. The author introduces the notion of a double cross product of monoidal categories as a generalization of double cross product of Hopf algebras, and explains some of the motivation from physics (the representation theory for double quantum groups).The Hopf algebra constructions are formulated in terms of...

Squared Hopf algebras and reconstruction theorems

Volodymyr Lyubashenko (1997)

Banach Center Publications

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Given an abelian 𝑉-linear rigid monoidal category 𝑉, where 𝑉 is a perfect field, we define squared coalgebras as objects of cocompleted 𝑉 ⨂ 𝑉 (Deligne's tensor product of categories) equipped with the appropriate notion of comultiplication. Based on this, (squared) bialgebras and Hopf algebras are defined without use of braiding. If 𝑉 is the category of 𝑉-vector spaces, squared (co)algebras coincide with conventional ones. If 𝑉 is braided, a braided Hopf algebra can be obtained...

From left modules to algebras over an operad: application to combinatorial Hopf algebras

Muriel Livernet (2010)

Annales mathématiques Blaise Pascal

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The purpose of this paper is two fold: we study the behaviour of the forgetful functor from 𝕊 -modules to graded vector spaces in the context of algebras over an operad and derive the construction of combinatorial Hopf algebras. As a byproduct we obtain freeness and cofreeness results for those Hopf algebras. Let 𝒪 denote the forgetful functor from 𝕊 -modules to graded vector spaces. Left modules over an operad 𝒫 are treated as 𝒫 -algebras in the category of 𝕊 -modules. We generalize...

Braided monoidal categories and Doi-Hopf modules for monoidal Hom-Hopf algebras

Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang (2016)

Colloquium Mathematicae

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We continue our study of the category of Doi Hom-Hopf modules introduced in [Colloq. Math., to appear]. We find a sufficient condition for the category of Doi Hom-Hopf modules to be monoidal. We also obtain a condition for a monoidal Hom-algebra and monoidal Hom-coalgebra to be monoidal Hom-bialgebras. Moreover, we introduce morphisms between the underlying monoidal Hom-Hopf algebras, Hom-comodule algebras and Hom-module coalgebras, which give rise to functors between the category of...

Spinors in braided geometry

Mićo Đurđević, Zbigniew Oziewicz (1996)

Banach Center Publications

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Let V be a ℂ-space, σ ∈ E n d ( V ⊗ 2 ) be a pre-braid operator and let F ∈ l i n ( V ⊗ 2 , ℂ ) . This paper offers a sufficient condition on (σ,F) that there exists a Clifford algebra Cl(V,σ,F) as the Chevalley F-dependent deformation of an exterior algebra C l ( V , σ , 0 ) ≡ V ∧ ( σ ) . If σ ≠ σ - 1 and F is non-degenerate then F is not a σ-morphism in σ-braided monoidal category. A spinor representation as a left Cl(V,σ,F)-module is identified with an exterior algebra over F-isotropic ℂ-subspace of V. We give a sufficient condition on braid σ that the spinor...

Local quasitriangular Hopf algebras.

Zhang, Shouchuan, Gould, Mark D., Zhang, Yao-Zhong (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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