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nLab > Latest Changes: super Lie algebra

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 20th 2009

    added a few references and links to super Lie algebra

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 11th 2017

    I have expanded the Definition-section at super Lie algebra, stating more variants of equivalent definitions. This is material taken from the more comprehensive lecture notes at geometry of physics – superalgebra.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 29th 2019

    added some minimum cross-link with Whitehead product

    diff, v29, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeDec 8th 2019

    added doi for:

    diff, v34, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 25th 2020

    added the statement (here) that super Lie algebras equipped with a lift to ℤ\mathbb{Z}-grading and with a choice of square-0 element in degree -1 are equivalently dg-Lie algebras

    diff, v38, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMay 25th 2020
    • (edited May 25th 2020)

    I have added some discussion (here) of the super Lie algebra of multilinear maps V ⊗ n→VV^{\otimes_n} \to V for any finite-dimensional vector space VV, following Palmkvist 13, 3.1, Lavau-Palmkvist 19, 2.4 (my proof of the super-Jacobi identity remains incomplete, despite the lengthy computation).

    The discussion culminates in the observation that “embedding tensors” are equivalently elements of square=0 and degree = -1 in this algebra, and hence are equivalently the datum to turn it into a dg-Lie algebra – supposedly (up to some restrictions and extensions) the “tensor hierarchy” induced by the embedding tensor. Which is a neat observation.

    This super Lie algebra ought to have some standard name? Palmkvist attributes it to

    • Isaiah L. Kantor, Graded Lie algebras, Trudy Sem. Vektor. Tenzor. Anal 15 (1970): 227-266.

    but I haven’t found an actual copy of this article yet.

    diff, v38, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeDec 11th 2020
    • (edited Dec 11th 2020)

    added pointer to today’s

    Will add to other related entries, too, such as Lie algebra cohomology and integrable forms

    diff, v41, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeApr 26th 2024

    added pointer to:

    diff, v48, current

1 to 8 of 8

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