dorsal/arxiv
View SchemaQuantization of Poisson groups -- II
| Authors | Fabio Gavarini |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9604007 |
| URL | https://arxiv.org/abs/q-alg/9604007 |
Abstract
Let $ G^\tau $ be a connected simply connected semisimple algebraic group, endowed with generalized Sklyanin-Drinfeld structure of Poisson group; let $ H^\tau $ be its dual Poisson group. By means of Drinfeld's double construction and dualization via formal Hopf algebras, we construct new quantum groups $ U_{q,\phi}^M ({\frak h}) $ --- dual of $ U_{q,\phi}^{M'} ({\frak g}) $ --- which yield infinitesimal quantization of $ H^\tau $ and $ G^\tau $; we study their specializations at roots of 1 (in particular, their classical limits), thus discovering new quantum Frobenius morphisms. The whole description dualize for $ H^\tau $ what was known for $ G^\tau $, completing the quantization of the pair $ (G^\tau,H^\tau) $.
{
"annotation_id": "73d724eb-f30e-47ae-9648-04389ee483b5",
"date_created": "2026-03-02T18:01:28.659000Z",
"date_modified": "2026-03-02T18:01:28.659000Z",
"file_hash": "cec2e16c9f829bd54955856f48f0b1e2c3802cd262a034ddf8fc79c883b3d168",
"private": false,
"record": {
"abstract": "Let $ G^\\tau $ be a connected simply connected semisimple algebraic group,\nendowed with generalized Sklyanin-Drinfeld structure of Poisson group; let $\nH^\\tau $ be its dual Poisson group. By means of Drinfeld\u0027s double construction\nand dualization via formal Hopf algebras, we construct new quantum groups $\nU_{q,\\phi}^M ({\\frak h}) $ --- dual of $ U_{q,\\phi}^{M\u0027} ({\\frak g}) $ ---\nwhich yield infinitesimal quantization of $ H^\\tau $ and $ G^\\tau $; we study\ntheir specializations at roots of 1 (in particular, their classical limits),\nthus discovering new quantum Frobenius morphisms. The whole description dualize\nfor $ H^\\tau $ what was known for $ G^\\tau $, completing the quantization of\nthe pair $ (G^\\tau,H^\\tau) $.",
"arxiv_id": "q-alg/9604007",
"authors": [
"Fabio Gavarini"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Quantization of Poisson groups -- II",
"url": "https://arxiv.org/abs/q-alg/9604007"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "62bf0392-759f-4848-91a2-4dc9303c3ab6",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}