dorsal/arxiv
View SchemaExplicit Hopf-Galois description of $SL_{e^{2i\pi/3}}$-induced Frobenius homomorphisms
| Authors | L. Dabrowski, P. M. Hajac, P. Siniscalco |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9708031 |
| URL | https://arxiv.org/abs/q-alg/9708031 |
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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"abstract": "The exact sequence of ``coordinate-ring\u0027\u0027 Hopf algebras A(SL(2,C)) -\u003e\nA(SL_q(2)) -\u003e A(F) determined by the Frobenius map Fr, and the same way\nobtained exact sequence of (quantum) Borel subgroups, are studied when q is a\ncubic root of unity. An A(SL(2,C))-linear splitting of A(SL_q(2)) making\nA(SL(2,C)) a direct summand of A(SL_q(2)) is constructed and used to prove that\nA(SL_q(2)) is a faithfully flat A(F)-Galois extension of A(SL(2,C)). A cocycle\nand coaction determining the bicrossed-product structure of the\nupper-triangular (Borel) quantum subgroup of A(SL_q(2)) are computed\nexplicitly.",
"arxiv_id": "q-alg/9708031",
"authors": [
"L. Dabrowski",
"P. M. Hajac",
"P. Siniscalco"
],
"categories": [
"q-alg",
"math-ph",
"math.MP",
"math.QA"
],
"title": "Explicit Hopf-Galois description of $SL_{e^{2i\\pi/3}}$-induced Frobenius homomorphisms",
"url": "https://arxiv.org/abs/q-alg/9708031"
},
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"variant": "snapshot-2026-03-01",
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