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An Introduction to Lie Groups

机译：撒谎群体概论

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This paper is made out of necessity as a doctoral student taking the exam from Lie groups. Using the literature suggested to me by the professor, I felt the need to, in addition to that literature, and since there was more superficial in that book with some remarks about the examples given in relation to the left group. I decided to try a little harder and collect as much literature as possible, both for the needs of me and the others who will take after me. Searching for literature in my mother tongue I could not find anything, in English as someone who comes from a small country like Montenegro, all I could find was through the internet. I decided to gather what I could find from the literature in my own way and to my observation and make this kind of work. The main content of this paper is to present the Lie group in the simplest way. Before and before I started writing or collecting about Lie groups, it was necessary to say something about groups and subgroups that are taught in basic studies in algebra. In them I cited several deficits and an example. The following content of the paper is related to Lie groups primarily concerning the definition of examples such as The General Linear Group GL(n, R) , The Complex General Linear Group GL(n, C) , The Special Linear Group SL(n, R)=SL(V) , The Complex Special Linear Group SL(n, C) , Unitary and Orthogonal Groups , Symplectic Group , The groups R*, C*, S~(1) and R~(n) and others. In addition, invariant vector fields and the exponential map and the lie algebra of a lie group. For me, this work has the significance of being useful to all who need it.
机译：本文符合来自谎言群体考试的博士生。使用教授向我建议的文献，我觉得还需要，除了那篇文学之外，由于该书中有更肤浅的表明，关于与左侧组有关的例子。我决定尽可能地尝试一点，尽可能多地收集文献，这都是为了我的需求和其他人会在我之后服用。在母语中寻找文学，我找不到任何东西，英语是来自像黑山这样的小国的人，我所能找到的只是通过互联网。我决定以自己的方式和我的观察来收集我可以从文学中找到的东西，并使这种工作。本文的主要内容是以最简单的方式呈现LIE组。在我开始写作或收集谎言群体之前和之前，有必要说一些关于代数基础研究中教授的群体和子组的些什么。在他们中，我引用了几种赤字和一个例子。本文的以下内容与主要关于实施例的定义的LIE组有关，例如通用线性组g1（n，r），特殊的线性组SL（n，r）= sl（v），复杂的特殊线性组sl（n，c），单一和正交组，杂项组， r *，c *，s〜（1）和r〜（n）等。此外，不变的矢量字段和指数地图和Lie Group的谎言代数。对我来说，这项工作具有对需要它的所有人有用的重要性。

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