Solutions of the Quantum-Yang-Baxter-Equation from Symmetric Spaces

Details Solutions of the Quantum-Yang-Baxter-Equation from Symmetric Spaces Solutions of the Quantum-Yang-Baxter-Equation from Symmetric Spaces

2001-07-03

arxiv.org/abs/math/0107018v1

Mathematics

Quantum Algebra

10 pages, amsfonts,amssymb,amsmath,latexsym

Scientific paper

We show that for each semi-Riemannian locally symmetric space the curvature tensor gives rise to a rational solution $r$ of the classical Yang-Baxter equation with spectral parameter. For several Riemannian globally symmetric spaces $M$ such as real, complex and quaternionic Grassmann manifolds we explicitly compute solutions $R$ of the quantum Yang Baxter equations (represented in the tangent spaces of $M$) which generalize the quantum $R$-matrix found by Zamolodchikov and Zamolodchikov in 1979.

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