Algebraic classical W-algebras and Frobenius manifolds

Yassir Ibrahim Dinar*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We consider Drinfeld–Sokolov bihamiltonian structure associated with a distinguished nilpotent elements of semisimple type and the space of common equilibrium points defined by its leading term. On this space, we construct a local bihamiltonian structure which forms an exact Poisson pencil, defines an algebraic classical W-algebra, admits a dispersionless limit, and its leading term defines an algebraic Frobenius manifold. This leads to a uniform construction of algebraic Frobenius manifolds corresponding to regular cuspidal conjugacy classes in irreducible Weyl groups.

Original languageEnglish
Article number115
JournalLetters in Mathematical Physics
Volume111
Issue number5
DOIs
Publication statusPublished - Oct 2021
Externally publishedYes

Keywords

  • Classical W-algebra
  • Common equilibrium points
  • Drinfeld–Sokolov reduction
  • Exact Poisson pencil
  • Frobenius manifolds
  • Nilpotent orbits in Lie algebras

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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