Polarization of generalized Nijenhuis torsions

TL;DR

This paper introduces the concept of polarization of generalized Nijenhuis torsions, establishing algebraic identities and demonstrating their importance in characterizing Haantjes modules of operator fields.

Contribution

It presents a novel notion of polarization for Nijenhuis torsions and links it to the structure of Haantjes modules, advancing the theoretical understanding.

Findings

Established algebraic identities for polarizations

Linked polarization to Haantjes module characterization

Provided new tools for studying operator fields

Abstract

In this work, we introduce the notion of polarization of generalized Nijenhuis torsions and establish several algebraic identities. We prove that these polarizations are relevant in the characterization of Haantjes $C^{\infty}$(M)-modules of operator fields.