Cohomology and automorphisms for a matched pair of 3-Lie algebras

Abstract

We begin by reviewing the definition of 3-Lie algebras and the fundamental concepts of matched pairs. Subsequently, we introduce the representation theory of matched pairs and define the semidirect product. Building on this foundation, we define the low-dimensional cohomology groups of matched pairs. In addition, we explore the infinitesimal deformations and abelian extensions of matched pairs. Finally, we examine the inducibility of automorphisms of matched pairs and present related results through the Wells exact sequence.