dorsal/arxiv
View SchemaColoured Hopf algebras
| Authors | C. Quesne |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9705019 |
| URL | https://arxiv.org/abs/q-alg/9705019 |
| Journal | Quantum Group Symposium at Group 21, eds. H.-D. Doebner and V. K. Dobrev (Heron Press, Sofia, 1997) 219-226 |
Abstract
Quite recently, a ``coloured'' extension of the Yang-Baxter equation has appeared in the literature and various solutions of it have been proposed. In the present contribution, we introduce a generalization of Hopf algebras, to be referred to as coloured Hopf algebras, wherein the comultiplication, counit, and antipode maps are labelled by some colour parameters. The latter may take values in any finite, countably infinite, or uncountably infinite set. A straightforward extension of the quasitriangularity property involves a coloured universal ${\cal R}$-matrix, satisfying the coloured Yang-Baxter equation. We show how coloured Hopf algebras can be constructed from standard ones by using an algebra isomorphism group, called colour group. Finally, we present two examples of coloured quantum universal enveloping algebras.
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"abstract": "Quite recently, a ``coloured\u0027\u0027 extension of the Yang-Baxter equation has\nappeared in the literature and various solutions of it have been proposed. In\nthe present contribution, we introduce a generalization of Hopf algebras, to be\nreferred to as coloured Hopf algebras, wherein the comultiplication, counit,\nand antipode maps are labelled by some colour parameters. The latter may take\nvalues in any finite, countably infinite, or uncountably infinite set. A\nstraightforward extension of the quasitriangularity property involves a\ncoloured universal ${\\cal R}$-matrix, satisfying the coloured Yang-Baxter\nequation. We show how coloured Hopf algebras can be constructed from standard\nones by using an algebra isomorphism group, called colour group. Finally, we\npresent two examples of coloured quantum universal enveloping algebras.",
"arxiv_id": "q-alg/9705019",
"authors": [
"C. Quesne"
],
"categories": [
"q-alg",
"math.QA"
],
"journal_ref": "Quantum Group Symposium at Group 21, eds. H.-D. Doebner and V. K.\n Dobrev (Heron Press, Sofia, 1997) 219-226",
"title": "Coloured Hopf algebras",
"url": "https://arxiv.org/abs/q-alg/9705019"
},
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