Supertetrahedra and superalgebras

Sergey M. Sergeev

doi:10.1063/1.3204504

Supertetrahedra and superalgebras

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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 풰q(glˆ(n∣m)) superalgebras and their representation theory.

Original language	English
Article number	083519
Pages (from-to)	1-21
Number of pages	21
Journal	Journal of Mathematics
Volume	50
Issue number	8
DOIs	https://doi.org/10.1063/1.3204504
Publication status	Published - Aug 2009

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10.1063/1.3204504

https://arxiv.org/pdf/0805.4653.pdf

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Supertetrahedra and superalgebras

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