課程資訊
 課程名稱 李代數二LIE ALGEBRA(Ⅱ) 開課學期 96-2 授課對象 理學院  數學系 授課教師 林紹雄 課號 MATH5127 課程識別碼 221 U4040 班次 學分 3 全/半年 半年 必/選修 選修 上課時間 星期五5,6(12:20~14:10)星期六2(9:10~10:00) 上課地點 新501 備註 先備知識:微積分、線代、代數.週六在舊數103.總人數上限：50人 課程簡介影片 核心能力關聯 核心能力與課程規劃關聯圖 課程大綱 為確保您我的權利,請尊重智慧財產權及不得非法影印 課程概述 Contents： The Lie Algebras have now become essential to many parts of mathematics, and theoretical physics, or quantum chemistry. This course will offer an introduction to this important field. We will start with the definitions of Lie algebras, like solvable, nilpotent, simple and semi-simple Lie algebras, etc., and their characterizations. We then proceed to classify all finite-dimensional simple Lie algebras, introducing the root systems and Dynkin diagrams. The typical classical Lie algebras, and exceptional Lie algebras will be introduced. Their representations by boson fields, or Fermion fields, or differential operators give different versions of the representation theory of these algebras. In the discussions of the representation theory, the theory of finite group representations will also be introduced. If the time permits, we will introduce the Kac-Moody algebras and the Virasoro algebras as examples of infinite-dimensional algebras. 課程目標 We shall emphasize more on the applications of the Lie algebras to other fields of science. Hopefully the students will appreciate the elegance of Lie algebras. 課程要求 Course prerequisite： Linear algebra, Calculus, Algebra. 預期每週課後學習時數 Office Hours 參考書目 III. Reference material ( textbook(s) )： (a) F. Iachello, Lie Algebras and Applications, Lecture note in Physics, 708(2006). (b) K. Erdman and M. Wildom, Introduction to Lie Algebras, Springer Undergraduate Mathematics Series, 2006. (c) H. Georgi, Lie Algebras in Particle Physics, Benjamin/Cumming (1982). (d) A. Boardman, D. O’Connor and P. Young, Symmetry and its Applications in Science, (1973). IV. Grading scheme： The students are required to give some talks on some chosen subjects in this field as a basis of their course grades. 指定閱讀 評量方式(僅供參考)
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