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Titlebook: Lie Groups, Lie Algebras, and Representations; An Elementary Introd Brian C. Hall Textbook Nov 20101st edition Springer Science+Business Me

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發(fā)表于 2025-3-21 16:46:22 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Lie Groups, Lie Algebras, and Representations
副標(biāo)題An Elementary Introd
編輯Brian C. Hall
視頻videohttp://file.papertrans.cn/586/585706/585706.mp4
概述Includes supplementary material:
叢書名稱Graduate Texts in Mathematics
圖書封面Titlebook: Lie Groups, Lie Algebras, and Representations; An Elementary Introd Brian C. Hall Textbook Nov 20101st edition Springer Science+Business Me
描述This book provides an introduction to Lie groups, Lie algebras, and repre- sentation theory, aimed at graduate students in mathematics and physics. Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it a useful addition to the literature. First, it treats Lie groups (not just Lie alge- bras) in a way that minimizes the amount of manifold theory needed. Thus, I neither assume a prior course on differentiable manifolds nor provide a con- densed such course in the beginning chapters. Second, this book provides a gentle introduction to the machinery of semi simple groups and Lie algebras by treating the representation theory of SU(2) and SU(3) in detail before going to the general case. This allows the reader to see roots, weights, and the Weyl group "in action" in simple cases before confronting the general theory. The standard books on Lie theory begin immediately with the general case: a smooth manifold that is also a group. The Lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. Th
出版日期Textbook Nov 20101st edition
關(guān)鍵詞Eigenvalue; Eigenvector; Lie algebra; Matrix; Permutation; Representation theory; Vector space; algebra; lin
版次1
doihttps://doi.org/10.1007/978-0-387-21554-9
issn_series 0072-5285
copyrightSpringer Science+Business Media New York 2003
The information of publication is updating

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沙發(fā)
發(fā)表于 2025-3-21 23:34:24 | 只看該作者
Lie Algebras and the Exponential Mappingx Lie group (Section 2.5) and is the mechanism for passing information from the Lie algebra to the Lie group. Since many computations are done much more easily at the level of the Lie algebra, the exponential is indispensable in studying (matrix) Lie groups.
板凳
發(fā)表于 2025-3-22 01:36:23 | 只看該作者
The Representations of ,(3) representation theory of SU(3). However, I feel that it is worthwhile to examine the case of SU(3) separately, before going on to the general theory. I feel this way partly because SU(3) is an important group in physics, but chiefly because the general semisimple theory is difficult to digest. Cons
地板
發(fā)表于 2025-3-22 05:02:59 | 只看該作者
Semisimple Lie Algebrasations can be described, similarly to sl(3; ?), by a “theorem of the highest weight.” We will not come to the representations themselves until the next chapter; in this chapter, we develop the structures needed to state the theorem of the highest weight. Although this chapter could be understood sim
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發(fā)表于 2025-3-22 08:45:04 | 只看該作者
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發(fā)表于 2025-3-22 12:58:51 | 只看該作者
More on Roots and Weightsabout root systems that are relevant to the understanding of semisimple Lie algebras but whose proofs involve only the root systems and not the Lie algebras from which they came. Therefore, it is convenient to separate the theory of root systems from Lie algebras.
7#
發(fā)表于 2025-3-22 19:11:27 | 只看該作者
implicitly, and at times explicitly, compare Japanese and Western approaches to bioethics. As this volume shows, there are similarities. There are also marked differences. The similarities reflect a common attempt outside of any particular culture to find morally justified bases for collaboration wh
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發(fā)表于 2025-3-22 22:55:08 | 只看該作者
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發(fā)表于 2025-3-23 02:59:20 | 只看該作者
Brian C. Hallome accessible to both diagnostic and manipulative intervention, the normative status of the human genome has become a directly practical, as well as a theoretical problem. For years, it and connected problems have been the subject of debate, not only amongst academics, but also politicians and lawy
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發(fā)表于 2025-3-23 05:52:18 | 只看該作者
Brian C. Hallen Kapitel gewonnenen analytischen Ergebnisse stützt, soll die ordnungspolitische Beurteilung des Verhaltens der exekutiven EG-Organe einleiten. Handel und Direktinvestitionen bilden bei dem sich akzelerierenden Proze? weltweiter ?konomischer Verflechtung komplement?re und ‘wirkungsgleiche’ internat
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