Supertetrahedra and superalgebras

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    In this paper we give a detailed classification scheme for three-dimensional quantum zero curvature representation and tetrahedron equations. This scheme includes both even and odd parity components; the resulting algebras of observables are either Bose q-oscillators or Fermi oscillators. Three-dimensional R-matrices intertwining variously oriented tensor products of Bose and Fermi oscillators and satisfying tetrahedron and supertetrahedron equations are derived. The 3d→2d compactification reproduces 풰q(glˆ(n∣m)) superalgebras and their representation theory.
    Original languageEnglish
    Article number083519
    Pages (from-to)1-21
    Number of pages21
    JournalJournal of Mathematics
    Issue number8
    Publication statusPublished - Aug 2009


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