Extensions of vertex algebras. Constructions and applications

This paper discusses the main known constructions of vertex operator algebras. The starting point is the lattice algebra. Screenings distinguish subalgebras of lattice algebras. Moreover, one can construct extensions of vertex algebras. Combining these constructions gives most of the known examples....

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Bibliographic Details
Published in:Russian mathematical surveys 2017-08, Vol.72 (4), p.707-763
Main Author: Feigin, B. L.
Format: Article
Language:English
Subjects:
Algebra
Operators (mathematics)
opers
quantum groups
screenings
vertex operator algebras
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Summary:This paper discusses the main known constructions of vertex operator algebras. The starting point is the lattice algebra. Screenings distinguish subalgebras of lattice algebras. Moreover, one can construct extensions of vertex algebras. Combining these constructions gives most of the known examples. A large class of algebras with big centres is constructed. Such algebras have applications to the geometric Langlands programme. Bibliography: 46 titles.
ISSN:0036-0279
1468-4829
DOI:10.1070/RM9778