%0 Journal Article
%A Reyes Nozaleda, Daniel
%A Tempesta, Piergiulio
%A Tondo, Giorgio
%T Generalized Nijenhuis torsions and block-diagonalization of operator fields
%D 2023
%@ 0938-8974
%U https://hdl.handle.net/20.500.14352/73182
%X 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.
%~