Bi-Hamiltonian Systems Of Minimal Poisson W-algebras
by
Minoru Wakimoto
Vol. 6 No. 4 (2011) P.463~P.483
ABSTRACT
In this note, we discuss bi-Hamiltonian structures of Poisson W-algebras of minimal
nilpotent elements and show that there always exist two kinds of bi-Hamiltonian pairs, which we call ``KdV type" and ``HD type" since
they are generalizations of the KdV and the Harry-Dym hierarches associated to the Virasoro Poisson vertex algebra.
KEYWORDS
Poisson vertex algebra, minimal Poisson W-algebra, bi-Hamiltonian pairs, Lenard scheme, evolution equation
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 17B65, 17B68, 17B69, 22E65, 37K30
MILESTONES
Received: 2011-05-30
Revised : 2011-08-01
Accepted: 2011-08-02
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