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2007.34: Integrable matrix equations related to pairs of compatible associative algebras

2007.34: A. V. Odesskii and V. V. Sokolov (2006) Integrable matrix equations related to pairs of compatible associative algebras. Journal of Physcis A: Mathematical and General, 39 (40). pp. 12447-12456. ISSN 0305-4470

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Abstract

We study associative multiplications in semi-simple 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 k-1}, \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 k-1} -type and integrable matrix ODEs and PDEs generated by them.

Item Type: Article MSC 2000 > 14 Algebraic geometryMSC 2000 > 17 Nonassociative rings and algebrasMSC 2000 > 32 Several complex variables and analytic spaces 2007.34 Miss Louise Stait 27 March 2007

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