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Coquasitriangular structures for extensions of Hopf algebras. Applications,

Journal Contribution - Journal Article

Let A E be an extension of Hopf algebras such that there exists a normal left A-module coalgebra map : 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, ) as follows: first, any such extension E is isomorphic to a unified product A H, for some unitary subcoalgebra H of E ([2]). 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, , 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 D(A,H) = A ?? H to be a coquasitriangular Hopf algebra. Several examples are worked out in
detail.
Journal: Glasgow Math. J.
ISSN: 0017-0895
Issue: 55
Pages: 201-215
Publication year:2013
Keywords:unified product, double cross product, coquasitriangular structure
  • Scopus Id: 84870872189