New Simple Lie Algebras in Characteristic 2

Sofiane Bouarroudj, Pavel Grozman, Alexei Lebedev, Dimitry Leites, Irina Shchepochkina

    Research output: Contribution to journalArticle

    Abstract

    Several improvements of the Kostrikin-Shafarevich method conjecturally producing all simple finite-dimensional Lie algebras over algebraically closed fields of any positive characteristic were recently suggested; the list of examples obtained by the improved method becomes richer but in characteristic 2 it is far from being saturated. We investigate one of the steps of our version of the method; in characteristic 2 we describe several new simple Lie algebras and interpret several other simple Lie algebras, previously known only as sums of their components, as Lie algebras of vector fields. Several new simple Lie superalgebras can be constructed from the newly found simple Lie algebras. We also describe one new simple Lie superalgebra in characteristic 3; it is the only simple Lie superalgebra missed in the approach taken in [6].

    Original languageEnglish (US)
    Pages (from-to)5695-5726
    Number of pages32
    JournalInternational Mathematics Research Notices
    Volume2016
    Issue number18
    DOIs
    StatePublished - Jan 1 2016

    Fingerprint

    Simple Lie Algebra
    Lie Superalgebra
    Lie Algebra
    Positive Characteristic
    Finite Dimensional Algebra
    Algebraically closed
    Vector Field

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Bouarroudj, S., Grozman, P., Lebedev, A., Leites, D., & Shchepochkina, I. (2016). New Simple Lie Algebras in Characteristic 2. International Mathematics Research Notices, 2016(18), 5695-5726. https://doi.org/10.1093/imrn/rnv327

    New Simple Lie Algebras in Characteristic 2. / Bouarroudj, Sofiane; Grozman, Pavel; Lebedev, Alexei; Leites, Dimitry; Shchepochkina, Irina.

    In: International Mathematics Research Notices, Vol. 2016, No. 18, 01.01.2016, p. 5695-5726.

    Research output: Contribution to journalArticle

    Bouarroudj, S, Grozman, P, Lebedev, A, Leites, D & Shchepochkina, I 2016, 'New Simple Lie Algebras in Characteristic 2', International Mathematics Research Notices, vol. 2016, no. 18, pp. 5695-5726. https://doi.org/10.1093/imrn/rnv327
    Bouarroudj S, Grozman P, Lebedev A, Leites D, Shchepochkina I. New Simple Lie Algebras in Characteristic 2. International Mathematics Research Notices. 2016 Jan 1;2016(18):5695-5726. https://doi.org/10.1093/imrn/rnv327
    Bouarroudj, Sofiane ; Grozman, Pavel ; Lebedev, Alexei ; Leites, Dimitry ; Shchepochkina, Irina. / New Simple Lie Algebras in Characteristic 2. In: International Mathematics Research Notices. 2016 ; Vol. 2016, No. 18. pp. 5695-5726.
    @article{825fd8aa0c2540878b241446f5af0786,
    title = "New Simple Lie Algebras in Characteristic 2",
    abstract = "Several improvements of the Kostrikin-Shafarevich method conjecturally producing all simple finite-dimensional Lie algebras over algebraically closed fields of any positive characteristic were recently suggested; the list of examples obtained by the improved method becomes richer but in characteristic 2 it is far from being saturated. We investigate one of the steps of our version of the method; in characteristic 2 we describe several new simple Lie algebras and interpret several other simple Lie algebras, previously known only as sums of their components, as Lie algebras of vector fields. Several new simple Lie superalgebras can be constructed from the newly found simple Lie algebras. We also describe one new simple Lie superalgebra in characteristic 3; it is the only simple Lie superalgebra missed in the approach taken in [6].",
    author = "Sofiane Bouarroudj and Pavel Grozman and Alexei Lebedev and Dimitry Leites and Irina Shchepochkina",
    year = "2016",
    month = "1",
    day = "1",
    doi = "10.1093/imrn/rnv327",
    language = "English (US)",
    volume = "2016",
    pages = "5695--5726",
    journal = "International Mathematics Research Notices",
    issn = "1073-7928",
    publisher = "Oxford University Press",
    number = "18",

    }

    TY - JOUR

    T1 - New Simple Lie Algebras in Characteristic 2

    AU - Bouarroudj, Sofiane

    AU - Grozman, Pavel

    AU - Lebedev, Alexei

    AU - Leites, Dimitry

    AU - Shchepochkina, Irina

    PY - 2016/1/1

    Y1 - 2016/1/1

    N2 - Several improvements of the Kostrikin-Shafarevich method conjecturally producing all simple finite-dimensional Lie algebras over algebraically closed fields of any positive characteristic were recently suggested; the list of examples obtained by the improved method becomes richer but in characteristic 2 it is far from being saturated. We investigate one of the steps of our version of the method; in characteristic 2 we describe several new simple Lie algebras and interpret several other simple Lie algebras, previously known only as sums of their components, as Lie algebras of vector fields. Several new simple Lie superalgebras can be constructed from the newly found simple Lie algebras. We also describe one new simple Lie superalgebra in characteristic 3; it is the only simple Lie superalgebra missed in the approach taken in [6].

    AB - Several improvements of the Kostrikin-Shafarevich method conjecturally producing all simple finite-dimensional Lie algebras over algebraically closed fields of any positive characteristic were recently suggested; the list of examples obtained by the improved method becomes richer but in characteristic 2 it is far from being saturated. We investigate one of the steps of our version of the method; in characteristic 2 we describe several new simple Lie algebras and interpret several other simple Lie algebras, previously known only as sums of their components, as Lie algebras of vector fields. Several new simple Lie superalgebras can be constructed from the newly found simple Lie algebras. We also describe one new simple Lie superalgebra in characteristic 3; it is the only simple Lie superalgebra missed in the approach taken in [6].

    UR - http://www.scopus.com/inward/record.url?scp=84994410025&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84994410025&partnerID=8YFLogxK

    U2 - 10.1093/imrn/rnv327

    DO - 10.1093/imrn/rnv327

    M3 - Article

    VL - 2016

    SP - 5695

    EP - 5726

    JO - International Mathematics Research Notices

    JF - International Mathematics Research Notices

    SN - 1073-7928

    IS - 18

    ER -