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Integrable matrix equations related to pairs of compatible associative algebras

Alexander Odesskii·Vladimir Sokolov
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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.

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Alexander Odesskii, Vladimir Sokolov. 2006-09-19. Integrable matrix equations related to pairs of compatible associative algebras. https://doi.org/10.1088/0305-4470/39/40/011

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