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(G,χϕ)-equivariant ϕ-coordinated quasi modules for vertex algebras.
- Source :
-
Journal of Algebra . Jan2022, Vol. 590, p26-60. 35p. - Publication Year :
- 2022
-
Abstract
- To give a unified treatment on the association of Lie algebras and vertex algebras, we study (G , χ ϕ) -equivariant ϕ -coordinated quasi modules for vertex algebras, where G is a group with χ ϕ a linear character of G and ϕ is an associate of the one-dimensional additive formal group. The theory of (G , χ ϕ) -equivariant ϕ -coordinated quasi modules for nonlocal vertex algebra is established in [10]. In this paper, we concentrate on the context of vertex algebras. We establish several conceptual results, including a generalized commutator formula and a general construction of vertex algebras and their (G , χ ϕ) -equivariant ϕ -coordinated quasi modules. Furthermore, for any conformal algebra C , we construct a class of Lie algebras C ˆ ϕ [ G ] and prove that restricted C ˆ ϕ [ G ] -modules are exactly (G , χ ϕ) -equivariant ϕ -coordinated quasi modules for the universal enveloping vertex algebra of C. As an application, we determine the (G , χ ϕ) -equivariant ϕ -coordinated quasi modules for affine and Virasoro vertex algebras. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 590
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 153417402
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2021.10.004