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  1. arXiv.org
    https://arxiv.org › abs

    LieART 2.0 -- A Mathematica Application for Lie Algebras and …

    LieART - A Mathematica Application for Lie Algebras and Representation ...
    Vanderbilt University Institutional Repository
    LieART 2.0 – A Mathematica application for Lie Algebras and ...
    INSPIRE
    LieART 2.0 – A Mathematica application for Lie Algeb…

    We present LieART 2.0 which contains substantial extensions to the Mathematica application LieART (Lie Algebras and Representation Theory) for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. The basic procedure is unchanged—it computes root systems of Lie algebras, weight systems and several other properties of irredu…

    We present LieART 2.0 which contains substantial extensions to the Mathematica application LieART (Lie Algebras and Representation Theory) for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. The basic procedure is unchanged—it computes root systems of Lie algebras, weight systems and several other properties of irreducible representations, but new features and procedures have been included to allow the extensions to be seamless. The new version of LieART continues to be user friendly. New extended tables of properties, tensor products and branching rules of irreducible representations are included in the supplementary material for use without Mathematica software. LieART 2.0 now includes the branching rules to special subalgebras for all classical and exceptional Lie algebras up to and including rank 15.

    Program summary

    Program Title: LieART 2.0

    CPC Library link to program files: http://dx.doi.org/10.17632/8vm7j67bwt.1

    Licensing provisions: GNU Lesser General Public License

    ScienceDirect

    The application of group theory to symmetries associated with physical systems is one of the most important tools of modern science. Examples abound in physics, chemistry and beyond into biology and engineering. Continuous groups in the form of Lie groups are all important in physics, with smaller Lie groups entering quantum mechanics, physical chemistry and condensed matter physics, while the full spectrum of Lie groups, i.e., the classical groups SU(N), SO(N) and Sp(2N) and the exceptional groups E6, E7, E8, F4 and G2, have all appeared in particle physics. Lie groups have had many other application in theoretical physics from gravity, to string theory, M-theory, F-theory, and beyond. In LieART [3] the focus is on Lie algebras of compact Lie groups that are most useful for particle physics. However, most of our results could easily be extended to the non-compact forms.

    LieART is a convenient easy to use Mathematica application to explore Lie groups and their algebras. It was designed to provide most of the Lie algebra information needed for particle physics model building. In particular it can find tensor product rules and irreducible representation (irrep) decompositions for Lie algebras found in Grand Unified Theories (GUTs) and other common extensions of the standard model. But LieART has also found application in many other areas of theoretical physics. LieART 2.0 is a response to the nee…

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    LieART is hosted by Hepforge, IPPP Durham. The LieART project home page is

    http://lieart.hepforge.org/

    and the LieART Mathematica application can be downloaded as archive from

    http://lieart.hepforge.org/downloads/

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    Start Mathematica and in the front end select the menu entry

    File → Install…

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    This section provides a tutorial introducing the most important and frequently used functions of LieART for Lie-algebra and representation-theory related calculations. The functions are introduced based on simple examples that can easily be modified and extended to the user’s desired application. Most examples use irreducible representations (irrep...

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