  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.
