dorsal/arxiv
View Schema$P_\infty$ algebra of KP, free fermions and 2-cocycle in the Lie algebra of pseudodifferential operators
| Authors | A. Yu. Orlov, P. Winternitz |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9701008 |
| URL | https://arxiv.org/abs/solv-int/9701008 |
| DOI | 10.1142/S0217979297001532 |
Abstract
The symmetry algebra $P_\infty = W_\infty \oplus H \oplus I_\infty$ of integrable systems is defined. As an example the classical Sophus Lie point symmetries of all higher KP equations are obtained. It is shown that one (``positive'') half of the point symmetries belongs to the $W_\infty$ symmetries while the other (``negative'') part belongs to the $I_\infty$ ones. The corresponing action on the tau-function is obtained for the positive part of the symmetries. The negative part can not be obtained from the free fermion algebra. A new embedding of the Virasoro algebra into $gl(\infty )$n describes conformal transformations of the KP time variables. A free fermion algebra cocycle is described as a PDO Lie algebra cocycle.
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"abstract": "The symmetry algebra $P_\\infty = W_\\infty \\oplus H \\oplus I_\\infty$ of\nintegrable systems is defined. As an example the classical Sophus Lie point\nsymmetries of all higher KP equations are obtained. It is shown that one\n(``positive\u0027\u0027) half of the point symmetries belongs to the $W_\\infty$\nsymmetries while the other (``negative\u0027\u0027) part belongs to the $I_\\infty$ ones.\nThe corresponing action on the tau-function is obtained for the positive part\nof the symmetries. The negative part can not be obtained from the free fermion\nalgebra. A new embedding of the Virasoro algebra into $gl(\\infty )$n describes\nconformal transformations of the KP time variables. A free fermion algebra\ncocycle is described as a PDO Lie algebra cocycle.",
"arxiv_id": "solv-int/9701008",
"authors": [
"A. Yu. Orlov",
"P. Winternitz"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1142/S0217979297001532",
"title": "$P_\\infty$ algebra of KP, free fermions and 2-cocycle in the Lie algebra of pseudodifferential operators",
"url": "https://arxiv.org/abs/solv-int/9701008"
},
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