Cohomology of Filippov n-Algebroids from the Perspective of Connection

This paper investigates the cohomology of Filippov n -algebroids, and discusses the cohomology of Filippov n -algebroids from the perspective of connection. By studying the derivations of Filippov n -algebroids, the Filippov multiderivations of degree p on the n -anchored bundle and the bracket, we establish the graded Lie algebra structure corresponding to the Filippov multiderivation on the n -anchored bundle. It is also proved that there exists a one-to-one correspondence between the 1 -order Filippov multiderivation satisfying \varphi ,\varphi =0 , i.e. \varphi \in \textDer_\nabla ^1(A) and the Filippov connection \nabla on n -anchored bundle (A\rightarrow M,\rho ) . Finally, using the graded Lie algebra (\textDer_\nabla ^*(A),\cdot ,\cdot ) , we introduce the cohomology of Filippov n -algebroids (\textC_\nabla ^*(A),\textδ_\nabla ^*) , and the corresponding cohomology groups \textH_\nabla ^*(A) are given.