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Integrability of invariant metrics on the Virasoro group

Constantin, Adrian LU ; Kolev, B and Lenells, Jonatan LU (2006) In Physics Letters. Section A: General, Atomic and Solid State Physics 350(1-2). p.75-80
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.
Please use this url to cite or link to this publication:
author
; and
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publishing date
type
Contribution to journal
publication status
published
subject
keywords
bi-Hamiltonian structures, Virasoro group
in
Physics Letters. Section A: General, Atomic and Solid State Physics
volume
350
issue
1-2
pages
75 - 80
publisher
Elsevier
external identifiers
  • wos:000234935400013
  • scopus:30644471049
ISSN
0375-9601
DOI
10.1016/j.physleta.2005.10.011
language
English
LU publication?
yes
id
216e1e1c-44a4-4b88-83b3-d8bc8f1e8178 (old id 418351)
date added to LUP
2016-04-01 16:38:15
date last changed
2021-10-03 04:01:29
@article{216e1e1c-44a4-4b88-83b3-d8bc8f1e8178,
  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.},
  author       = {Constantin, Adrian and Kolev, B and Lenells, Jonatan},
  issn         = {0375-9601},
  language     = {eng},
  number       = {1-2},
  pages        = {75--80},
  publisher    = {Elsevier},
  series       = {Physics Letters. Section A: General, Atomic and Solid State Physics},
  title        = {Integrability of invariant metrics on the Virasoro group},
  url          = {http://dx.doi.org/10.1016/j.physleta.2005.10.011},
  doi          = {10.1016/j.physleta.2005.10.011},
  volume       = {350},
  year         = {2006},
}