Abstract
In this paper we analyze the matrix differential system X' = [N,X2], where N is skew-symmetric and X(0) is symmetric. We prove that it is isospectral and that it is endowed with a Poisson structure, and we discuss its invariants and Casimirs. Formulation of the Poisson problem in a Lie-Poisson setting, as a flow on a dual of a Lie algebra, requires a computation of its faithful representation. Although the existence of a faithful representation, assured by the Ado theorem and a symbolic algorithm, due to de Graaf, exists for the general computation of faithful representations of Lie algebras, the practical problem of forming a "tight" representation, convenient for subsequent analytic and numerical work, belongs to numerical algebra. We solve it for the Poisson structure corresponding to the equation X' = [N,X2].
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
