nLab classical r-matrix

Idea

An $R$-matrix is a solution to a Yang-Baxter equation:

A classical r-matrix is a solution of classical Yang-Baxter equation.

(A quantum R-matrix is a solution to the quantum Yang-Baxter equation.)

Related entries

• Lie bialgebra

• Poisson Lie group

Yang-Baxter equations

• classical Yang-Baxter equation

• quantum Yang-Baxter equation

• dynamical quantum Yang-Baxter equation

• associative Yang-Baxter equation

• infinitesimal braid relation

• set theoretic Yang-Baxter equation

• quasitriangular bialgebra

References

• M. A. Semenov-Tyan-Shanskii, Classical r-matrices and quantization, J. Math. Sciences 31:6 (1985), 3411-3416, doi; Classical r-matrices and the method of orbits, J. Math. Sciences 28:4 (1985), 513-524, doi

• V. G. Drinfel'd, Quantum groups, Proceedings of the International Congress of Mathematicians 1986, Vol. 1, 798–820, AMS 1987, djvu:1.3M, pdf:2.5M

• Victor Mouquin, The Fock-Rosly Poisson structure as defined by a quasitriangular r-matrix, arxiv/1610.01782