On an Isospectral Lie–Poisson System and Its Lie Algebra

被引：0

作者：

Anthony M. Bloch

Arieh Iserles

机构：

[1] Department of Mathematics,

[2] University of Michigan,undefined

[3] Ann Arbor,undefined

[4] MI 48109,undefined

[5] Department of Applied Mathematics and Theoretical Physics,undefined

[6] Centre for Mathematical Sciences,undefined

[7] University of Cambridge,undefined

[8] Wilberforce Road,undefined

[9] Cambridge CB3 0WA,undefined

来源：

Foundations of Computational Mathematics | 2006年 / 6卷

关键词：

Isospectral flows; Poisson system; Lie algebra; Faithful representations;

D O I：

暂无

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学科分类号：

摘要：

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].

引用

页码：121 / 144

页数：23