Explicit Hopf-Galois description of $SL_{e^{2iπ/3}}$-induced Frobenius homomorphisms

L. Dabrowski; P. M. Hajac; P. Siniscalco

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Explicit Hopf-Galois description of $SL_{e^{2iπ/3}}$-induced Frobenius homomorphisms

L. Dabrowski·P. M. Hajac·P. Siniscalco

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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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BibTeX RIS

L. Dabrowski, P. M. Hajac, P. Siniscalco. 1998-09-28. Explicit Hopf-Galois description of $SL_{e^{2iπ/3}}$-induced Frobenius homomorphisms. https://arxiv.org/abs/q-alg/9708031

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