Dirac reductions and Classical W-algebras

Abstract

In the first part of this paper, we generalize Dirac reduction to the extent of non-local Poisson vertex superalgebra and non-local SUSY Poisson vertex algebra cases. Next, we modify this reduction so that we explain the structures of classical W-superalgebras and SUSY classical W-algebras in terms of the modified Dirac reduction.

References in corpus (16)

• Quantum Reduction for Affine Superalgebras
• Finite vs. affine W-algebras
• Poisson vertex algebras in the theory of Hamiltonian equations
• Representation theory of finite W algebras
• Yangian realisations from finite W algebras
• Supersymmetric vertex algebras
• Classical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras
• Non-local Poisson structures and applications to the theory of integrable systems
• Classical W-algebras for gl_N and associated integrable Hamiltonian hierarchies
• Classical affine W-algebras and the associated integrable Hamiltonian hierarchies for classical Lie algebras
• Twisted Yangians and folded W-algebras
• Dirac reduction for Poisson vertex algebras
• On the Completeness of the Set of Classical W-Algebras Obtained from DS Reductions
• Quantum Hamiltonian Reduction in Superspace Formalism
• Supersymmetric W-algebras
• Classical affine W-superalgebras via generalized Drinfeld-Sokolov reductions and related integrable systems