$\mathcal{W}$ algebras are L${}_{\infty }$ algebras

Abstract

It is shown that the closure of the infinitesimal symmetry transformations underlying classical $\mathcal{W}$ algebras give rise to L${}_{\infty }$ algebras with in general field dependent gauge parameters. Therefore, the class of well understood $\mathcal{W}$ algebras provides highly non-trivial examples of such strong homotopy Lie-algebras. We develop the general formalism for this correspondence and apply it explicitly to the classical ${\mathcal{W}}_3$ algebra.

15 pages; v2: typos corrected, minor changes

References in corpus (3)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Wilsonian Effective Action of Superstring Theory