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  • A. L. AGORE (a1)

Let AE be an extension of Hopf algebras such that there exists a normal left A-module coalgebra map π : EA 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 AH, 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 AH 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) = AτH to be a coquasitriangular Hopf algebra. Several examples are worked out in detail.

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1. A. L. Agore and G. Militaru , Extending structures II: The quantum version, J. Algebra 336 (2011), 321341.

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12. S. Majid , Quantum groups and quantum probability, in Quantum probability and related topics, vol. 6 (World Scienntific, River Edge, NJ, 1991), 333358.

14. M. Takeuchi , Representations of the Hopf algebra U(n), in Hopf algebras and generalizations, Contemporary Mathematics, vol. 441, (Amer. Math. Soc., Providence, RI, 2007), 155174.

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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