Super-tetrahedra and super-algebras

Details Super-tetrahedra and super-algebras Super-tetrahedra and super-algebras

2008-05-30

arxiv.org/abs/0805.4653v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX, 27 pages

Scientific paper

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 super-tetrahedron equations are derived. The 3d->2d compactification reproduces U_q(gl(n|m)) super-algebras and their representation theory.

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