Symmetric matrices and maximal Nijenhuis pencils

doi:10.4213/sm9862e

Andrei Yur'evich Konyaev

Symmetric matrices and maximal Nijenhuis pencils

Algebra and Number Theory

A Nijenhuis pencil is a linear subspace of the space of $(1,1)$ tensor field which consists of Nijenhuis operators. The problem of the description of maximal (by inclusion) Nijenhuis pencils containing a subpencil of dimension $n(n+1)/2$ such that the operators in it are - in some system of coordinates - constant symmetric matrices, is solved. Two such pencils turn out to exist, both of which arise in a natural way in applications, for example, in the theory of infinite-dimensional integrable systems. Bibliography: 6 titles.

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Symmetric matrices and maximal Nijenhuis pencils

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