Local Properties Of Block-type Lie Algebra

Lie algebra of Block type B(q)is an important class of infinite dimensional Lie algebras with important applications in mathematics and physics.Virasoro-like algebra is a class of subalgebra of Lie algebra of Block type B(0),it is named because it is similar to the structure of Virasoro algebra.2-local derivations and 2-local automorphisms represent the local property of algebras,they are important research contents in the structure theory of algebras and have attracted many scholars’ attention in recent years.In this paper,we study the local property of some Lie algebras of Block type.Specifically,this article mainly studies the 2-local derivations of Lie algebra of Block type B(q)in the case of q?Z,as well as the 2-local derivations and 2-local automorphisms of Virasoro-like algebras.Firstly,it proves that all 2-local derivations of Lie algebra of Block type B(q)are derivations when q?Z.Secondly,it proves that all 2-local derivations of the Virasoro-like algebra are derivations,and all 2-local automorphisms are automorphisms.