Freely generated vertex algebras and non-linear Lie conformal algebras

Abstract

We introduce the notion of a non--linear Lie conformal superalgebra and prove a PBW theorem for its universal enveloping vertex algebra. We also show that conversely any graded freely generated vertex algebra is the universal enveloping algebra of a non--linear Lie conformal superalgebra. This correspondence will be applied in the subsequent work to the problem of classification of finitely generated simple graded vertex algebras.

38 pages

References in corpus (1)

• Field Algebras

Cited by in corpus (28)

• Finite vs. affine W-algebras
• Trialities of $\mathcal{W}$-algebras
• Howe Pairs in the Theory of Vertex Algebras
• Universal two-parameter ${\mathcal{W}}_{\infty }$-algebra and vertex algebras of type $\mathcal{W}(2,3,\dots ,N)$
• Universal two-parameter even spin ${\mathcal{W}}_{\infty }$-algebra
• Chiral de Rham complex on Riemannian manifolds and special holonomy
• Singular support of a vertex algebra and the arc space of its associated scheme
• $N=4$ superconformal algebras and diagonal cosets
• Computation of cohomology of Lie conformal and Poisson vertex algebras
• Introduction to Vertex Algebras
• Generalized parafermions of orthogonal type
• Unitary representations of the ${\mathcal{W}}_3$-algebra with $c\ge 2$
• A remark on simplicity of vertex algebras and Lie conformal algebras
• A remark on the $C_2$-cofiniteness condition on vertex algebras
• On even spin $W_{\infty }$
• On the structure of W-algebras in type A
• Classification of rank two Lie conformal algebras
• Ito's conjecture and the coset construction for ${\mathcal{W}}^k(\mathfrak{sl}(3|2))$
• Galilean $W_3$ algebra
• T-duality and the exotic chiral de Rham complex
• Left-symmetric algebras, or pre-Lie algebras in geometry and physics
• Non-linear Lie conformal algebras with three generators
• Quantized Reductions and Irreducible Representations of W-Algebras
• $\hslash$-Vertex algebras and chiralization of star products
• Vertex Algebras and Commutative Algebras
• Formal vertex laws associated to Lie conformal algebras
• ${\mathrm{G}}_2$ holonomy manifolds are superconformal
• Zhu's Algebra of a C1-cofinite Vertex Algebra