Integrable matrix equations related to pairs of compatible associative algebras
Abstract
We study associative multiplications in semisimple associative algebras over {\bb C} compatible with the usual one. An interesting class of such multiplications is related to the affine Dynkin diagrams of \skew5\tilde{A}_{2 k1}, \tilde{D}_{k}, \tilde{E}_{6}, \tilde{E}_{7} , and \tilde{E}_{8} type. In this paper we investigate in detail the multiplications of the \skew5\tilde{A}_{2 k1} type and integrable matrix ODEs and PDEs generated by them.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 October 2006
 DOI:
 10.1088/03054470/39/40/011
 arXiv:
 arXiv:math/0604574
 Bibcode:
 2006JPhA...39..011O
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory;
 High Energy Physics  Theory;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 17B80;
 17B63;
 32L81;
 14H70
 EPrint:
 12 pages, Latex