Vertex $F$-Algebras and Their Associated Lie Algebra
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911378089967616 |
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| author | Upmeier, Markus |
| author_facet | Upmeier, Markus |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21390 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Vertex $F$-Algebras and Their Associated Lie Algebra Upmeier, Markus Quantum Algebra 17B69 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. |
| title | Vertex $F$-Algebras and Their Associated Lie Algebra |
| topic | Quantum Algebra 17B69 |
| url | https://arxiv.org/abs/2503.21390 |