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COQUASITRIANGULAR STRUCTURES FOR EXTENSIONS OF HOPF ALGEBRAS. APPLICATIONS

Published online by Cambridge University Press:  02 August 2012

A. L. AGORE
A. L. AGORE*
Affiliation:
Faculty of Engineering, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium e-mail: ana.agore@vub.ac.be, ana.agore@gmail.com
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Abstract

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Let A ⊆ E be an extension of Hopf algebras such that there exists a normal left A-module coalgebra map π : E → A that splits the inclusion. We shall describe the set of all coquasitriangular structures on the Hopf algebra E in terms of the datum (A, E, π) as follows: first, any such extension E is isomorphic to a unified product A ⋉ H, for some unitary subcoalgebra H of E (A. L. Agore and G. Militaru, Unified products and split extensions of Hopf algebras, to appear in AMS Contemp. Math.). Then, as a main theorem, we establish a bijective correspondence between the set of all coquasitriangular structures on an arbitrary unified product A ⋉ H and a certain set of datum (p, τ, u, v) related to the components of the unified product. As the main application, we derive necessary and sufficient conditions for Majid's infinite-dimensional quantum double Dλ(A, H) = A ⋈τH to be a coquasitriangular Hopf algebra. Several examples are worked out in detail.

Keywords

16T1016T0516S40
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 1 , January 2013 , pp. 201 - 215
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

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