Supersymmetric W-algebras

Abstract

We explain a general theory of W-algebras in the context of supersymmetric vertex algebras. We describe the structure of W-algebras associated with odd nilpotent elements of Lie superalgebras in terms of their free generating sets. As an application, we produce explicit free generators of the W-algebra associated with the odd principal nilpotent element of the Lie superalgebra \(\mathfrak {gl}(n+1|n)\).

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Correspondence to Uhi Rinn Suh.

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Molev, A., Ragoucy, E. & Suh, U.R. Supersymmetric W-algebras. Lett Math Phys 111, 6 (2021). https://doi.org/10.1007/s11005-020-01346-1

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Keywords

  • Supersymmetric Vertex algebras
  • W superalgebras
  • Free generating sets

Mathematics Subject Classification

  • 17B35
  • 17B68
  • 17B69
  • 17B70