Towards Vertex Algebras of Krichever-Novikov Type, Part I
K. J. Linde (U. Munich/ U. Liverpool)

TL;DR
This paper explores the construction of vertex algebra-like structures from Krichever-Novikov algebras, proposing a new definition of Krichever-Novikov type vertex algebras and analyzing their relation to classical vertex algebras.
Contribution
It introduces a novel class of vertex algebras based on Krichever-Novikov algebras and discusses their connection to traditional vertex algebra theory.
Findings
A representation of the Krichever-Novikov algebra yields a state field correspondence similar to classical vertex algebras.
A new definition of Krichever-Novikov type vertex algebras is proposed.
The relation between Krichever-Novikov type vertex algebras and standard vertex algebras is analyzed.
Abstract
It is shown that a certain representation of the Heisenberg type Krichever-Novikov algebra gives rise to a state field correspondence that is quite similar to the vertex algebra structure of the usual Heisenberg algebra. Finally a definition of Krichever-Novikov type vertex algebras is proposed and its relation to vertex algebras is discussed.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Rings, Modules, and Algebras
