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.
|Number of pages||21|
|Journal||Journal of Mathematics|
|Publication status||Published - Aug 2009|