Explicit Hopf-Galois description of $SL_{e^{2i\pi/3}}$-induced Frobenius homomorphisms
Dabrowski, L. ; Hajac, P. M. ; Siniscalco, P.
arXiv, 9708031 / Harvested from arXiv
Text on arXiv
The exact sequence of ``coordinate-ring'' Hopf algebras A(SL(2,C)) -> A(SL_q(2)) -> A(F) determined by the Frobenius map Fr, and the same way obtained exact sequence of (quantum) Borel subgroups, are studied when q is a cubic root of unity. An A(SL(2,C))-linear splitting of A(SL_q(2)) making A(SL(2,C)) a direct summand of A(SL_q(2)) is constructed and used to prove that A(SL_q(2)) is a faithfully flat A(F)-Galois extension of A(SL(2,C)). A cocycle and coaction determining the bicrossed-product structure of the upper-triangular (Borel) quantum subgroup of A(SL_q(2)) are computed explicitly.
Publié le : 1997-08-29
Classification:  Mathematics - Quantum Algebra,  Mathematical Physics 
@article{9708031,
     author = {Dabrowski, L. and Hajac, P. M. and Siniscalco, P.},
     title = {Explicit Hopf-Galois description of $SL\_{e^{2i\pi/3}}$-induced Frobenius
  homomorphisms},
     journal = {arXiv},
     volume = {1997},
     number = {0},
     year = {1997},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9708031}
}

Dabrowski, L.; Hajac, P. M.; Siniscalco, P. Explicit Hopf-Galois description of $SL_{e^{2i\pi/3}}$-induced Frobenius
  homomorphisms. arXiv, Tome 1997 (1997) no. 0, . http://gdmltest.u-ga.fr/item/9708031/