RT Journal Article
T1 Haantjes algebras and diagonalization
A1 Tempesta, Piergiulio
A1 Tondo, Giorgio
AB 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.
PB Elsevier
SN 0393-0440
YR 2021
FD 2021-03
LK https://hdl.handle.net/20.500.14352/7994
UL https://hdl.handle.net/20.500.14352/7994
LA eng
NO © 2021 ElsevierThe research of P. T. has been supported by the research project PGC2018-094898-B-I00, Ministerio de Ciencia, Innovacion y Universidades, Spain, and by the ICMAT Severo Ochoa project, Spain SEV-2015-0554, Ministerio de Ciencia, Innovacion y Universidades, Spain. P. T. and G. T. are members of Gruppo Nazionale di Fisica Matematica (GNFM) of INDAM.
NO Ministerio de Ciencia, Innovación y Universidades (MICINN)
NO Centros de Excelencia Severo Ochoa (MICINN)
DS Docta Complutense
RD 3 may 2024