Geodesic
COQUASITRIANGULAR STRUCTURES FOR EXTENSIONS OF HOPF ALGEBRAS. APPLICATIONS
Glasgow mathematical journal, Tome 55 (2013) no. 1, pp. 201-215

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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.
DOI : 10.1017/S0017089512000444
Mots-clés : 16T10, 16T05, 16S40 
AGORE, A. L. COQUASITRIANGULAR STRUCTURES FOR EXTENSIONS OF HOPF ALGEBRAS. APPLICATIONS. Glasgow mathematical journal, Tome 55 (2013) no. 1, pp. 201-215. doi: 10.1017/S0017089512000444
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     title = {COQUASITRIANGULAR {STRUCTURES} {FOR} {EXTENSIONS} {OF} {HOPF} {ALGEBRAS.} {APPLICATIONS}},
     journal = {Glasgow mathematical journal},
     pages = {201--215},
     year = {2013},
     volume = {55},
     number = {1},
     doi = {10.1017/S0017089512000444},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000444/}
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