$\mathcal{W}$ 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.

arXiv comment15 pages; v2: typos corrected, minor changes

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Cited by in corpus (4)

• On the Uniqueness of L${}_{\infty }$ bootstrap: Quasi-isomorphisms are Seiberg-Witten Maps
• Leibniz-Chern-Simons Theory and Phases of Exceptional Field Theory
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• On the Existence of an L${}_{\infty }$ structure for the Super-Virasoro Algebra