dorsal/arxiv
View SchemaThe centre of the graph and moduli algebras at roots of 1
| Authors | S. A. Frolov |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9602036 |
| URL | https://arxiv.org/abs/q-alg/9602036 |
| DOI | 10.1007/s002200050542 |
| Journal | Commun.Math.Phys. 200 (1999) 599-619 |
Abstract
The structure of the centres ${\cal Z}(\Lg)$ and ${\cal Z}(\Mg)$ of the graph algebra ${\cal L}_g(sl_2)$ and the moduli algebra ${\cal M}_g(sl_2)$ is studied at roots of 1. It it shown that ${\cal Z}(\Lg)$ can be endowed with the structure of the Poisson graph algebra. The elements of $Spec({\cal Z}(\Mg))$ are shown to satisfy the defining relation for the holonomies of a flat connection along the cycles of a Riemann surface. The irreducible representations of the graph algebra are constructed.
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"abstract": "The structure of the centres ${\\cal Z}(\\Lg)$ and ${\\cal Z}(\\Mg)$ of the graph\nalgebra ${\\cal L}_g(sl_2)$ and the moduli algebra ${\\cal M}_g(sl_2)$ is studied\nat roots of 1. It it shown that ${\\cal Z}(\\Lg)$ can be endowed with the\nstructure of the Poisson graph algebra. The elements of $Spec({\\cal Z}(\\Mg))$\nare shown to satisfy the defining relation for the holonomies of a flat\nconnection along the cycles of a Riemann surface. The irreducible\nrepresentations of the graph algebra are constructed.",
"arxiv_id": "q-alg/9602036",
"authors": [
"S. A. Frolov"
],
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"q-alg",
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"doi": "10.1007/s002200050542",
"journal_ref": "Commun.Math.Phys. 200 (1999) 599-619",
"title": "The centre of the graph and moduli algebras at roots of 1",
"url": "https://arxiv.org/abs/q-alg/9602036"
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