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00925njm 22002777a 4500 dc Tempesta, Piergiulio author Tondo, Giorgio author 2021-03 We introduce the notion of Haantjes algebra: It consists of an assignment of a family of operator fields on a differentiable manifold, each of them with vanishing Haantjes torsion. They are also required to satisfy suitable compatibility conditions. Haantjes algebras naturally generalize several known interesting geometric structures, arising in Riemannian geometry and in the theory of integrable systems. At the same time, as we will show, they play a crucial role in the theory of diagonalization of operators on differentiable manifolds. Assuming that the operators of a 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 general, non-semisimple case, they acquire simultaneously, in a suitable local chart, a block-diagonal form. (C) 2020 Elsevier B.V. All rights reserved. 0393-0440 10.1016/j.geomphys.2020.103968 https://hdl.handle.net/20.500.14352/7994 http://dx.doi.org/10.1016/j.geomphys.2020.103968 https://www.sciencedirect.com/ Haantjes algebras and diagonalization