Extensions and deformations of 3-Lie algebras with higher derivations

Abstract:

      Higher derivations on a 3-Lie algebra generalize higher-order derivatives. We call a tuple consisting of 3-Lie algebra and a higher derivation on it by a 3-LieHDer pair. We define cohomology for 3-LieHDer pairs with coefficients in a representation. Next, we study abelian extensions of a 3-LieHDer pair and relate them with the second cohomology group of the 3-LieHDer pair. Finally, we consider formal deformations of 3-LieHDer pairs that are governed by the cohomology with self-coefficient.