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arXiv · 2503.21390

Vertex $F$-Algebras and Their Associated Lie Algebra

Markus Upmeier
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Abstract

Vertex $F$-algebras are a deformation of the concept of an ordinary vertex algebra in which the additive formal group law is replaced by an arbitrary formal group law $F$. The main theorem of this paper constructs a Lie algebra from a vertex $F$-algebra - for the additive formal group law, this extends Borcherds' well-known construction for ordinary vertex algebras. Our construction involves the new concept of an $F$-residue and some other new algebraic concepts, which are deformations of familiar concepts for the special case of an additive formal group law.

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Markus Upmeier. 2025-03-27. Vertex $F$-Algebras and Their Associated Lie Algebra. https://doi.org/10.3842/sigma.2026.004

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