Weyl Groups And Geometric Setting Of Lie Algebras Of Cartan Type

This thesis mainly investigate the Weyl groups and semisimple orbits of Lie algebras of Cartan type, as well as the geometry related to Jacobson-Witt algebra. The main contents are listed below:Chapter 4 focuses on the Weyl groups and semisimple orbits for the re-stricted Cartan type Lie algebras, say type W, S and H. Chapter 5 obtains the conjugation classes of complete Borel subalgerbas of Jacobson-Witt algebra. In chapter 6,7 and 8, we firstly describe the homogeneous flag varieties, flag vari-eties and Springer varieties, and then investigate their propositions. Chapter 9 is the geometry of Witt algebra. The last chapter obtains the conjugation classes of complete Borel subalgebra of Special algebras under certain condition.