dorsal/arxiv
View SchemaDeforming the Lie algebra of vector fields on $S^1$ inside the Poisson algebra on $\dot T^*S^1$
| Authors | V. Ovsienko, C. Roger |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9707007 |
| URL | https://arxiv.org/abs/q-alg/9707007 |
| DOI | 10.1007/s002200050473 |
Abstract
We study deformations of the standard embedding of the Lie algebra $\Vect(S^1)$ of smooth vector fields on the circle, into the Lie algebra of functions on the cotangent bundle $T^*S^1$ (with respect to the Poisson bracket). We consider two analogous but different problems: (a) formal deformations of the standard embedding of $\Vect(S^1)$ into the Lie algebra of functions on $\dot T^*S^1:=T^*S^1\setminusS^1$ which are Laurent polynomials on fibers, and (b) polynomial deformations of the $\Vect(S^1)$ subalgebra inside the Lie algebra of formal Laurent series on $\dot T^*S^1$.
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"abstract": "We study deformations of the standard embedding of the Lie algebra\n$\\Vect(S^1)$ of smooth vector fields on the circle, into the Lie algebra of\nfunctions on the cotangent bundle $T^*S^1$ (with respect to the Poisson\nbracket). We consider two analogous but different problems: (a) formal\ndeformations of the standard embedding of $\\Vect(S^1)$ into the Lie algebra of\nfunctions on $\\dot T^*S^1:=T^*S^1\\setminusS^1$ which are Laurent polynomials on\nfibers, and (b) polynomial deformations of the $\\Vect(S^1)$ subalgebra inside\nthe Lie algebra of formal Laurent series on $\\dot T^*S^1$.",
"arxiv_id": "q-alg/9707007",
"authors": [
"V. Ovsienko",
"C. Roger"
],
"categories": [
"q-alg",
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],
"doi": "10.1007/s002200050473",
"title": "Deforming the Lie algebra of vector fields on $S^1$ inside the Poisson algebra on $\\dot T^*S^1$",
"url": "https://arxiv.org/abs/q-alg/9707007"
},
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