Research On A Kind Of Block - Type Lie Algebra

Lie algebra of Block type is R.Block during the 1958 doctoral introduced a class of infinite-dimensional simple Lie algebra. Later, many scholars to studied it and extended.Scholars has been given several different definitions of Lie algebra of Block type B(q) in the study. In this paper, We studied a new Lie algebra of Block type B(p, q) and the structure theory of B(p, q). By studying the finite element and local nilpotent element of B(p, q), we characterize the automorphism of B(p, q). Because of B(p, q) is a finitely generated Z-graded Lie algebra, we characterize derivations of B(p, q) in this feature. In this paper, we enriched and improved the structure theory of Lie algebra of Block type B(p, q).