Integrability of invariant metrics on the Virasoro group

Adrian Constantin; B Kolev; Jonatan Lenells

doi:10.1016/j.physleta.2005.10.011

Integrability of invariant metrics on the Virasoro group

Adrian Constantin, B Kolev, Jonatan Lenells

Mathematics (Faculty of Sciences)

Research output: Contribution to journal › Article › peer-review

Abstract

Each right-invariant metric on the Virasoro group induces a Hamiltonian vector field on the dual of the Lie algebra Dir equipped with the canonical Lie-Poisson structure. We show that the Hamiltonian vector fields X-k induced by the metrics given at the identity by the H-k Sobolev inner products, k >= 0, are bi-Hamiltonian relative to a modified Lie-Poisson structure only for k = 0 and k = 1. (c) 2005 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	75-80
Journal	Physics Letters. Section A: General, Atomic and Solid State Physics
Volume	350
Issue number	1-2
DOIs	https://doi.org/10.1016/j.physleta.2005.10.011
Publication status	Published - 2006

Subject classification (UKÄ)

Mathematics

Free keywords

bi-Hamiltonian structures
Virasoro group

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10.1016/j.physleta.2005.10.011

Cite this

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title = "Integrability of invariant metrics on the Virasoro group",

abstract = "Each right-invariant metric on the Virasoro group induces a Hamiltonian vector field on the dual of the Lie algebra Dir equipped with the canonical Lie-Poisson structure. We show that the Hamiltonian vector fields X-k induced by the metrics given at the identity by the H-k Sobolev inner products, k >= 0, are bi-Hamiltonian relative to a modified Lie-Poisson structure only for k = 0 and k = 1. (c) 2005 Elsevier B.V. All rights reserved.",

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T1 - Integrability of invariant metrics on the Virasoro group

AU - Constantin, Adrian

AU - Kolev, B

AU - Lenells, Jonatan

PY - 2006

Y1 - 2006

N2 - Each right-invariant metric on the Virasoro group induces a Hamiltonian vector field on the dual of the Lie algebra Dir equipped with the canonical Lie-Poisson structure. We show that the Hamiltonian vector fields X-k induced by the metrics given at the identity by the H-k Sobolev inner products, k >= 0, are bi-Hamiltonian relative to a modified Lie-Poisson structure only for k = 0 and k = 1. (c) 2005 Elsevier B.V. All rights reserved.

AB - Each right-invariant metric on the Virasoro group induces a Hamiltonian vector field on the dual of the Lie algebra Dir equipped with the canonical Lie-Poisson structure. We show that the Hamiltonian vector fields X-k induced by the metrics given at the identity by the H-k Sobolev inner products, k >= 0, are bi-Hamiltonian relative to a modified Lie-Poisson structure only for k = 0 and k = 1. (c) 2005 Elsevier B.V. All rights reserved.

KW - bi-Hamiltonian structures

KW - Virasoro group

U2 - 10.1016/j.physleta.2005.10.011

DO - 10.1016/j.physleta.2005.10.011

M3 - Article

SN - 0375-9601

VL - 350

SP - 75

EP - 80

JO - Physics Letters. Section A: General, Atomic and Solid State Physics

JF - Physics Letters. Section A: General, Atomic and Solid State Physics

IS - 1-2

ER -

Integrability of invariant metrics on the Virasoro group

Abstract

Subject classification (UKÄ)

Free keywords

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