李群李代数及相关的几何与代数结构

Abstract: In this project, we use the theory of Lie groups and Lie algebras to study some related geometric and algebraic problems. We mainly consider the following problems: Homogeneous parakaehler manifolds and dipolarizations in Lie algebras; certain rings of highest weight vectors; the groups of isometries of Finsler spaces; totally geodesic submanifolds of Riemannian symmetric spaces; the structure of Novikov algebras. We obtain the global classification of semisimple homogeneous parakaehler manifolds; prove the stability of certain rings of highest weight vectors; prove that the group of isometries of a Finslet space is a Lie group; obtain the.classification in the exceptional cases of the totally geodesic submanifolds of Riemannian symmetric spaces related to two commutative Cartan involutions; obtain the classification of low-dimensional.Novikov algebras and their realizations. This project have published 21 papers and 13 of them have been cited by Sci

李群，李代数及其相关的几何与代数结构是理论数学中重要的研究课题，与数学，物理等学科的许多领域密切相关。本项目将侧重于用代数方法解决近年来引人注目的一系列几何问题。即通过李代数的双极化来研究齐性仿凯勒流形，通过李代数相容的左对称代数研究流形上的仿射结构，通过对李群李代数的自同构的研究了解对称空间子流形的某些性质与结构。