Haantjes algebras and diagonalization

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dc.contributor.authorTempesta, Piergiulio
dc.contributor.authorTondo, Giorgio
dc.date.accessioned2023-06-17T09:02:10Z
dc.date.available2023-06-17T09:02:10Z
dc.date.issued2021-03
dc.description© 2021 Elsevier The 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.
dc.description.abstractWe 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.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipMinisterio de Ciencia, Innovación y Universidades (MICINN)
dc.description.sponsorshipCentros de Excelencia Severo Ochoa (MICINN)
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/64861
dc.identifier.doi10.1016/j.geomphys.2020.103968
dc.identifier.issn0393-0440
dc.identifier.officialurlhttp://dx.doi.org/10.1016/j.geomphys.2020.103968
dc.identifier.relatedurlhttps://www.sciencedirect.com/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/7994
dc.journal.titleJournal of geometry and physics
dc.language.isoeng
dc.publisherElsevier
dc.relation.projectIDPGC2018-094898-B-I00
dc.relation.projectIDSEV-2015-0554
dc.rights.accessRightsopen access
dc.subject.cdu51-73
dc.subject.keywordHaantjes tensor
dc.subject.keywordHaantjes manifolds
dc.subject.keywordHigher Nijenhuis torsions
dc.subject.ucmFísica-Modelos matemáticos
dc.subject.ucmFísica matemática
dc.titleHaantjes algebras and diagonalization
dc.typejournal article
dc.volume.number160
dspace.entity.typePublication
relation.isAuthorOfPublication46e9a666-a5cf-44c3-8726-7cbe2c61bd1a
relation.isAuthorOfPublication.latestForDiscovery46e9a666-a5cf-44c3-8726-7cbe2c61bd1a
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