Lie Groups
Lie Groups
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通讯作者：
J. S. Milne
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作者：
J. S. Milne
代数群理论可以被描述为李群理论的一部分，它只能用多项式(不能收敛的幂级数)来发展，因此适用于任何领域。或者，它是不需要分析的基本部分。正如我们将看到的，它实际上捕捉到了李群理论的一个重要部分。在这一章中，k、D、R或C。拓扑群G的单位分支被表示为G。所有的向量空间和表示都是有限维的。在这一章中，约化代数群不需要连通。[本章仅有部分摘要。最后，它将解释代数群和李群之间的确切关系；解释如何从实代数群和复代数群的相应理论中推导出约化李群的理论及其表示；足够的基本材料来提供对李群理论的完整独立介绍。]
The theory of algebraic groups can be described as that part of the theory of Lie groups that can be developed using only polynomials (not convergent power series), and hence works over any field. Alternatively, it is the elementary part that doesn't require analysis. As we'll see, it does in fact capture an important part of the theory of Lie groups. Throughout this chapter, k D R or C. The identity component of a topological group G is denoted by G C. All vectors spaces and representations are finite-dimensional. In this chapter, reductive algebraic groups are not required to be connected. [Only a partial summary of this chapter exists. Eventually it will include an explanation of the exact relation between algebraic groups and Lie groups; an explanation of how to derive the theory of reductive Lie groups and their representations from the corresponding theory for real and complex algebraic groups; enough of the basic material to provide a complete independent introduction to the theory of Lie groups.]