2014
DOI: 10.1007/s00220-014-2103-0
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Dirac Reduction for Poisson Vertex Algebras

Abstract: Abstract. We construct an analogue of Dirac's reduction for an arbitrary local or non-local Poisson bracket in the general setup of non-local Poisson vertex algebras. This leads to Dirac's reduction of an arbitrary non-local Poisson structure. We apply this construction to an example of a generalized Drinfeld-Sokolov hierarchy.

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Cited by 21 publications
(16 citation statements)
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“…In the case when f is a minimal nilpotent element we get after a reduction an integrable Hamiltonian equation on 2hˇ− 3 functions. In a forthcoming publication [DSKV13] we construct for both cases the second Poisson structure, which is non-local, via an analogue of Dirac reduction [Dir50].…”
Section: Introductionmentioning
confidence: 99%
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“…In the case when f is a minimal nilpotent element we get after a reduction an integrable Hamiltonian equation on 2hˇ− 3 functions. In a forthcoming publication [DSKV13] we construct for both cases the second Poisson structure, which is non-local, via an analogue of Dirac reduction [Dir50].…”
Section: Introductionmentioning
confidence: 99%
“…The H-Poisson structure does not induce a PVA λ-bracket on W/J K , and in order to obtain the second Poisson structure on it we have to apply Dirac's reduction, developed in [DSKV13].…”
mentioning
confidence: 99%
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“…Thus, in [DSKV14a] we proved that the YO hierarchy is obtained by Dirac reduction from the minimal sl 3 generalized Drinfeld-Sokolov hierarchy, and, as a result, we gave in formulas (8.4) and (8.5) two compatible Poisson structures for the YO hierarchy. The latter were found in [Che92].…”
mentioning
confidence: 60%
“…Our main observation in this regard is that the s-vector m-constrained KP hierarchy is isomorphic to the Dirac reduction by conformal weight 1 fields of the generalized Drinfeld-Sokolov hierarchy [DSKV14a,DSKV13], associated to the Lie algebra g = sl m+s and its nilpotent element f corresponding to the partition (m, 1, . .…”
mentioning
confidence: 99%