Dirac reduction for Poisson vertex algebras

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.

31 pages. Corrected some typos and added missing equations in Section 8

References in corpus (3)

• Classical W-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents
• Some remarks on non-commutative principal ideal rings
• Singular degree of a rational matrix pseudodifferential operator

Cited by in corpus (10)

• Classical W-algebras for gl_N and associated integrable Hamiltonian hierarchies
• Double Poisson vertex algebras and non-commutative Hamiltonian equations
• Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras
• Classical affine W-algebras and the associated integrable Hamiltonian hierarchies for classical Lie algebras
• Classical W-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents
• A new scheme of integrability for (bi)Hamiltonian PDE
• Local and non-local multiplicative Poisson vertex algebras and differential-difference equations
• Integrability of Dirac reduced bi-Hamiltonian equations
• Singular degree of a rational matrix pseudodifferential operator
• Dirac reductions and Classical W-algebras