A method of constructing braided Hopf algebras | Zendy

Tianshui Ma | Zendy; Shuanhong Wang | Zendy; Shaoxian Xu | Zendy

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A method of constructing braided Hopf algebras

Author(s) -

Tianshui Ma,

Shuanhong Wang,

Shaoxian Xu

Publication year - 2010

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1002053m

Subject(s) - hopf algebra , mathematics , tensor product , action (physics) , quasitriangular hopf algebra , tensor algebra , algebra over a field , representation theory of hopf algebras , pure mathematics , tensor (intrinsic definition) , multiplication (music) , product (mathematics) , construct (python library) , projection (relational algebra) , quantum group , combinatorics , filtered algebra , division algebra , geometry , computer science , physics , algorithm , quantum mechanics , programming language

Let A and B be two Hopf algebras and R ( Hom(B ( A, A ( B), the twisted tensor product Hopf algebra A#RB was introduced by S. Caenepeel et al in [3] and further studied in our recent work [6]. In this paper we give the necessary and sufficient conditions for A#RB to be a Hopf algebra with a projection. Furthermore, a braided Hopf algebra A is constructed by twisting the multiplication of A through a (γ, R)-pair (A, B). Finally we give a method to construct Radford's biproduct directly by defining the module action and comodule action from the twisted tensor biproduct. 2010 Mathematics Subject Classifications. 16W30. .

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