Symplectic Groups and Symplectic Algebras
Dr. Meng-kiat Chuah
|Keywords:||辛群與辛代數;辛群;辛代數;symplectic groups and symplectic algebras;symplectic groups;symplectic algebras|
A Lie group is a manifold G along with a group structure, such that the group operations are smooth. The tangent space of G at its identity is called the Lie algebra of G. In this thesis, we use linear algebra to study the matrix groups. These are groups formed by square matrices, and so certain feature of Lie groups can be computed more directly. Using these results, we study the structure theory of a type of matrix groups called the symplectic group. The contents of this thesis are arranged as follows : In Chapter 1, we introduce the matrix groups and some of their properties. As is often the case in Lie theory, we study their Lie algebras in Chapter 2. Then we consider the topological and algebraic properties of the matrix groups in Chapter 3. In Chapter 4, we introduce the symplectic group. This is followed by the study of its Cartan subalgebra in apter 5, and its root system in Chapter 6.
|Appears in Collections:||Thesis|