3 years ago

Haantjes Algebras and Diagonalization.

Giorgio Tondo, Piergiulio Tempesta

We propose the notion of Haantjes algebra, which consists of an assignment of a family of fields of operators over a differentiable manifold, with vanishing Haantjes torsion and satisfying suitable compatibility conditions among each others. Haantjes algebras naturally generalize several known interesting geometric structures, arising in Riemannian geometry and in the theory of integrable systems. At the same time, they play a crucial role in the theory of diagonalization of operators on differentiable manifolds.

Whenever the elements of an Haantjes algebra are semisimple and commute, we shall prove that there exists a set of local coordinates where all operators can be diagonalized simultaneously. Moreover, in the non-semisimple case, they acquire simultaneously a block-diagonal form.

Publisher URL: http://arxiv.org/abs/1710.04522

DOI: arXiv:1710.04522v2

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