Integrable matrix equations related to pairs of compatible associative algebras
arXiv:math/0604574 · doi:10.1088/0305-4470/39/40/011
Abstract
We study associative multiplications in semi-simple associative algebras over C compatible with the usual one. An interesting class of such multiplications is related to the affine Dynkin diagrams of A, D, E-type. In this paper we investigate in details the multiplications of the A-type and integrable matrix ODEs and PDEs generated by them.
12 pages, Latex