Super-tetrahedra and super-algebras

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

LaTeX, 27 pages

References in corpus (6)

• Zamolodchikov's Tetrahedron Equation and Hidden Structure of Quantum Groups
• Quantum geometry of 3-dimensional lattices
• Quantum Geometry of 3-Dimensional Lattices and Tetrahedron Equation
• Quantization of three-wave equations
• Ansatz of Hans Bethe for a two-dimensional Bose gas
• Simplified tetrahedron equations: Fermionic realization

Cited by in corpus (13)

• Solutions of the T-system and Baxter equations for supersymmetric spin chains
• Tetrahedron Equation and Quantum R Matrices for Spin Representations of B^{(1)}_n, D^{(1)}_n and D^{(2)}_{n+1}
• The pentagon relation and incidence geometry
• Quantum Geometry of 3-Dimensional Lattices and Tetrahedron Equation
• An Ising-type formulation of the six-vertex model
• Integrable 3D lattice model in M-theory
• Solution of tetrahedron equation and cluster algebras
• Classical integrable field theories in discrete 2+1 dimensional space-time
• Tetrahedron and 3D reflection equation from PBW bases of the nilpotent subalgebra of quantum superalgebras
• Non-commutative q-Painleve VI equation
• Tetrahedron Equation and Quantum $R$ Matrices for $q$-Oscillator Representations Mixing Particles and Holes
• Tetrahedron equations, boundary states and hidden structure of U_q(D_n^1)
• Ground states of Heisenberg evolution operator in discrete three-dimensional space-time and quantum discrete BKP equations