Super-tetrahedra and super-algebras

Sergey Sergeev

Super-tetrahedra and super-algebras

Sergey Sergeev

Research output: Contribution to conference (non-published works) › Paper

Abstract

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 Uq((n∣m)) superalgebras and their representation theory.

Original language	English
Pages	1-28
Number of pages	28
Publication status	Published - 2008

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abstract = "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 Uq((n∣m)) superalgebras and their representation theory.",

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