Explicit Hopf-Galois description of $SL_{e^{2i\pi/3}}$-induced Frobenius homomorphisms
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Publication:6503066
arXivq-alg/9708031MaRDI QIDQ6503066
L. Dabrowski, Piotr M. Hajac, Pasquale Siniscalco
Abstract: 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.
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