Cohomology and deformations of Filippov algebroids

TL;DR

This paper develops a cohomological framework for studying deformations of Filippov algebroids, introducing a DGLA structure, Nijenhuis operators, and analyzing finite order deformations.

Contribution

It defines a differential graded Lie algebra for Filippov algebroids and characterizes their deformations using cohomology and Nijenhuis operators, advancing the understanding of their deformation theory.

Findings

Defined a DGLA for Filippov algebroids

Characterized trivial deformations via Nijenhuis operators

Discussed extension of finite order deformations

Abstract

In this article, we study the deformations of Filippov algebroids. We define a differential graded Lie algebra (in short DGLA) for a Filippov algebroid by introducing the notion of Filippov multiderivations for a vector bundle. Later on, we discuss deformations of a Filippov algebroid in terms of low-dimensional cohomology associated to this DGLA. We define Nijenhuis operators on Filippov algebroids and characterize trivial deformations of Filippov algebroids in terms of these operators. In the end, we define finite order deformations and discuss the problem of extending a given finite order deformation to a deformation of a higher order.