Double Derivations Of Block-type Lie Algebras And Their Application

The derivation of Lie algebras is an important research content in the structure theory of Lie algebras.The biderivation is a kind of generalized derivation which can be directly applied to the linear commutative mapping of Lie algebras and the structure of commutative post-Lie algebras.Block type Lie algebras are a class of infinite dimensional simple Lie algebras introduced by Block in 1958 and later found to have important applications in mathematics and physics.Many scholars have studied the structure and representation theory of Block type Lie algebras and extended it to more types of Block type Lie algebras.In this paper,we will study the biderivations of a class of Block type Lie algebras and prove that the biderivations are all inner biderivations.As applications,the linear commutative mappings and the commutative post-Lie algebraic structures of the Lie algebra of Block type are given.