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Russian Mathematical Surveys, 2017, Volume 72, Issue 4, Pages 707–763
DOI: https://doi.org/10.1070/RM9778 (Mi rm9778) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Extensions of vertex algebras. Constructions and applications

B. L. Feigin

National Research University "Higher School of Economics", International Laboratory of Representation Theory and Mathematical Physics
English version PDF (817 kB) Citations (6)
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DOI: https://doi.org/10.1070/RM9778
Abstract: 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.
Keywords: vertex operator algebras, screenings, opers, quantum groups.
Funding agency Grant number
Russian Science Foundation 16-11-10316
This work was supported by the Russian Science Foundation under grant no. 16-11-10316.
Received: 10.04.2017
Russian version:
Uspekhi Matematicheskikh Nauk, 2017, Volume 72, Issue 4(436), Pages 131–190
DOI: https://doi.org/10.4213/rm9778
Bibliographic databases:
Document Type: Article
UDC: 512
MSC: Primary 17B69, 17B80, 81R10; Secondary 81R50
Language: English
Original paper language: Russian
Citation: B. L. Feigin, “Extensions of vertex algebras. Constructions and applications”, Uspekhi Mat. Nauk, 72:4(436) (2017), 131–190; Russian Math. Surveys, 72:4 (2017), 707–763
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/rm/v72/i4/p131
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:714
    Russian version PDF:162
    English version PDF:44
    References:67
    First page:59
     
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