Left-symmetric Algebraic Structures On Some Lie Algebra

Infinite dimension Lie algebra is an important research of Lie algebra.This papermainly focuses on a kind of Lie algebra named left-symmetrical algebraic structurethat is relevant to Witt algebra.In the second and the third chapters,we have given the Laurent polynomialalgebra A and consistent order of several kinds of left-symmetric algebraic structureof A's son of a guide Lie algebra.Then follow Rota-Baxter operator in general linearLie algebra gl₂(C) as a result of the complex field2×2matrix combined withalgebra,and we also have given some compatible left-symmetrical algebra structurein4-dimensions, and the related adjacent Lie algebra structure.The fourth chapter introduces the compatible disorder of non-graded left-symme-trical algebraic structures on the Witt algebra and its compatible conditions:xm xn=f(m, n)xm+n+g1(m, n)x_m+n+θ1+g₂(m, n)x_m+n+θ2, m, n∈Z,while f is acomplex-value function on Z×Z,and g1(m, n) is polynomial on Z×Z,g2(m, n) is anonzero rational complex-value function on Z×Z,θ₁, θ₂are both diferent nonzerointegers.