dorsal/arxiv
View SchemaBoundary solutions of the quantum Yang-Baxter equation and solutions in three dimensions
| Authors | Murray Gerstenhaber, Anthony Giaquinto |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9710033 |
| URL | https://arxiv.org/abs/q-alg/9710033 |
Abstract
Boundary solutions to the quantum Yang-Baxter (qYB) equation are defined to be those in the boundary of (but not in) the variety of solutions to the ``modified'' qYB equation, the latter being analogous to the modified classical Yang-Baxter (cYB) equation. We construct, for a large class of solutions $r$ to the modified cYB equation, explicit ``boundary quantizations'', i.e., boundary solutions to the qYB equation of the form $I+tr+ t^2r_{2} + ...$. In the last section we list and give quantizations for all classical r-matrices in $sl(3) \wedge sl(3)$.
{
"annotation_id": "a0680916-de41-451c-ae2f-fa2f9ef8284c",
"date_created": "2026-03-02T18:01:28.825000Z",
"date_modified": "2026-03-02T18:01:28.825000Z",
"file_hash": "a0e645ced9edd95f737213fc8693c2ab948a4a9236f1f6f520881d56e1326397",
"private": false,
"record": {
"abstract": "Boundary solutions to the quantum Yang-Baxter (qYB) equation are defined to\nbe those in the boundary of (but not in) the variety of solutions to the\n``modified\u0027\u0027 qYB equation, the latter being analogous to the modified classical\nYang-Baxter (cYB) equation. We construct, for a large class of solutions $r$ to\nthe modified cYB equation, explicit ``boundary quantizations\u0027\u0027, i.e., boundary\nsolutions to the qYB equation of the form $I+tr+ t^2r_{2} + ...$. In the last\nsection we list and give quantizations for all classical r-matrices in $sl(3)\n\\wedge sl(3)$.",
"arxiv_id": "q-alg/9710033",
"authors": [
"Murray Gerstenhaber",
"Anthony Giaquinto"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Boundary solutions of the quantum Yang-Baxter equation and solutions in three dimensions",
"url": "https://arxiv.org/abs/q-alg/9710033"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "2b71a757-ff31-48d3-8cce-96a1ffa379dc",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}