Braided Logarithmic Vertex Algebras

We study a family of algebras defined using a locally-finite endomorphism called a braiding map. When the braiding map is semi-simple, the algebra is a generalized vertex algebra, while when the braiding map is locally-nilpotent we have a logarithmic vertex algebra. We describe a method that associa...

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Bibliographic Details
Published in:arXiv.org 2024-06
Main Authors: Bakalov, Bojko, Villarreal, Juan J
Format: Article
Language:English
Subjects:
Algebra
Braiding
Logarithms
Online Access:Get full text
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Summary:We study a family of algebras defined using a locally-finite endomorphism called a braiding map. When the braiding map is semi-simple, the algebra is a generalized vertex algebra, while when the braiding map is locally-nilpotent we have a logarithmic vertex algebra. We describe a method that associates to these algebras non-local Poisson vertex algebras, and we use this relation to build a new example of a generalized vertex algebra motivated by the non-linear Schr\"odinger non-local Poisson vertex algebra
ISSN:2331-8422