Hypermatrix factors for string and membrane junctions

Yuhan Fang, Shir Levkowitz, Hisham Sati, Daniel Thompson

    Research output: Contribution to journal › Article

    Abstract

    The adjoint representations of the Lie algebras of the classical groups SU(n), SO(n) and Sp(n) are, respectively, tensor, antisymmetric and symmetric products of two vector spaces, and hence are matrix representations. We consider the analogous products of three vector spaces and study when they appear as summands in Lie algebra decompositions. The Z3-grading of the exceptional Lie algebras provides such summands and provides representations of classical groups on hypermatrices. The main natural application is a formal study of 3-junctions of strings and membranes. Generalizations are also considered.

    Original languageEnglish (US)
    Article number505401
    JournalJournal of Physics A: Mathematical and Theoretical
    Volume43
    Issue number50
    DOIs
    StatePublished - Dec 17 2010

    Fingerprint

    Algebra
    Lie Algebra
    algebra
    vector spaces
    strings
    Membrane
    Strings
    Classical Groups
    Vector spaces
    membranes
    Membranes
    Vector space
    Symmetric Product
    Adjoint Representation
    Matrix Representation
    Grading
    Antisymmetric
    products
    Tensors
    Tensor

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Statistics and Probability
    • Modeling and Simulation
    • Mathematical Physics
    • Physics and Astronomy(all)

    Cite this

    Hypermatrix factors for string and membrane junctions. / Fang, Yuhan; Levkowitz, Shir; Sati, Hisham; Thompson, Daniel.

    In: Journal of Physics A: Mathematical and Theoretical, Vol. 43, No. 50, 505401, 17.12.2010.

    Research output: Contribution to journal › Article

    Fang, Y, Levkowitz, S, Sati, H & Thompson, D 2010, 'Hypermatrix factors for string and membrane junctions', Journal of Physics A: Mathematical and Theoretical, vol. 43, no. 50, 505401. https://doi.org/10.1088/1751-8113/43/50/505401
    Fang Y, Levkowitz S, Sati H, Thompson D. Hypermatrix factors for string and membrane junctions. Journal of Physics A: Mathematical and Theoretical. 2010 Dec 17;43(50). 505401. https://doi.org/10.1088/1751-8113/43/50/505401
    Fang, Yuhan ; Levkowitz, Shir ; Sati, Hisham ; Thompson, Daniel. / Hypermatrix factors for string and membrane junctions. In: Journal of Physics A: Mathematical and Theoretical. 2010 ; Vol. 43, No. 50.
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