Classical Lie Groups

摘要: In this chapter, we apply the general theory to classical matrix groups such as \(\mathop {\mathrm {GL}}\nolimits _{n}({\mathbb{C}}), \mathop {\rm SL}\nolimits SO}\nolimits Sp}\nolimits _{2n}({\mathbb{C}})\), and some of their real forms provide explicit structural topological information. We will start with compact forms, i.e., U{}}\nolimits _{n}({\mathbb{K}})\) SU}\nolimits _{n}({\mathbb{K}})\), where \({\mathbb{K}}\) is ℝ, ℂ, or ℍ, since many results can be reduced groups.