書目名稱 | Lie Groups, Lie Algebras, and Representations | 副標(biāo)題 | An Elementary Introd | 編輯 | Brian C. Hall | 視頻video | http://file.papertrans.cn/586/585706/585706.mp4 | 概述 | Includes supplementary material: | 叢書名稱 | Graduate Texts in Mathematics | 圖書封面 |  | 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 | doi | https://doi.org/10.1007/978-0-387-21554-9 | issn_series | 0072-5285 | copyright | Springer Science+Business Media New York 2003 |
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