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課程名稱 |
近世代數一
Modern Algebra (Ⅰ) |
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開課學期 |
112-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
佐藤信夫 |
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課號 |
MATH5001 |
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課程識別碼 |
221EU6140 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
星期三6,7(13:20~15:10)星期五6,7(13:20~15:10) |
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上課地點 |
新304新304 |
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備註 |
本課程以英語授課。
總人數上限：30人 |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
The contents include the following: Groups and their actions, Irreducible representations, Schur's lemma, Complete reducibility, Group rings, Wedderburn's theorem, Characters, Orthogonality relations, Tensor product of representations, Restriction and induction, Representation of symmetric groups, Young tableaux, Schur-Weyl duality, Lie groups, Lie algebras, Universal enveloping algebra |
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課程目標 |
This course aims to give an introduction to basic topics on representation theory of finite groups and Lie algebras. We will not just discuss the general theories, but also take close looks at particularly important examples to have more concrete understandings of the theory. For the part of the representation theory of finite groups, we will put special focus on the representation theory of symmetric groups, and its relation to finite dimensional representations of general linear groups, along with some amusing combinatorics related to the theory. |
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課程要求 |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
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參考書目 |
William Fulton and Joe Harris, "Representation Theory, A First Course",
Jean-Pierre Serre, "Linear Representation of Finite Groups" |
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評量方式
(僅供參考) |
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