Generalized Nijenhuis torsions and block-diagonalization of operator fields

The theory of generalized Nijenhuis torsions, which extends the classical notions due to Nijenhuis and Haantjes, offers new tools for the study of normal forms of operator fields. We prove a general result ensuring that, given a family of commuting operator fields whose generalized Nijenhuis torsion...

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Bibliographic Details
Authors: Reyes Nozaleda, Daniel, Tempesta, Piergiulio, Tondo, Giorgio
Format: article
Publication Date:2023
Country:España
Institution:Universidad Complutense de Madrid (UCM)
Repository:Docta Complutense
Language:English
OAI Identifier:oai:docta.ucm.es:20.500.14352/73182
Online Access:https://hdl.handle.net/20.500.14352/73182
Access Level:Open access
Keyword:51-73
Haantjes
Systems
Física-Modelos matemáticos
Física matemática
Description
Summary:The theory of generalized Nijenhuis torsions, which extends the classical notions due to Nijenhuis and Haantjes, offers new tools for the study of normal forms of operator fields. We prove a general result ensuring that, given a family of commuting operator fields whose generalized Nijenhuis torsion of level m vanishes, there exists a local chart where all operators can be simultaneously block-diagonalized. We also introduce the notion of generalized Haantjes algebra, consisting of operators with a vanishing higher-level torsion, as a new algebraic structure naturally generalizing standard Haantjes algebras.