Skip to main content
×
Home
    • Aa
    • Aa

COQUASITRIANGULAR STRUCTURES FOR EXTENSIONS OF HOPF ALGEBRAS. APPLICATIONS

  • A. L. AGORE (a1)
Abstract
Abstract

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.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

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

4. S. Caenepeel , G. Militaru and S. Zhu , Frobenius and separable functors for generalized module categories and nonlinear equations, Lecture Notes in Mathematics, vol. 1787 (Springer Verlag, Berlin, 2002).

5. Y. Doi and M. Takeuchi , Multiplication alteration by two-cocycles, Commun. Algebra. 22 (14) (1994), 57155732.

7. Z. Jiao and R. Wisbauer , The braided structures for ω-smash coproduct Hopf algebras, J. Algebra 287 (2) (2005), 474495.

10. R. Larson and J. Towber , Two dual classes of bialgebras related to the concepts of “quantum groups” and “quantum Lie algebras,” Commun. Algebra 19 (1991), 32953345.

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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 6 *
Loading metrics...

Abstract views

Total abstract views: 46 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th July 2017. This data will be updated every 24 hours.