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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