学部・大学院区分
Undergraduate / Graduate

多・博前

時間割コード
Registration Code

3211092

科目区分
Course Category

Ａ類Ⅱ（専門科目）
Category A-2

科目名　【日本語】
Course Title

数理科学特論Ⅵ

科目名　【英語】
Course Title

Topics in Mathematical ScienceⅥ

コースナンバリングコード
Course Numbering Code

担当教員　【日本語】
Instructor

CHAN Aaron kay yam ○

担当教員　【英語】
Instructor

CHAN Aaron kay yam ○

単位数
Credits

開講期・開講時間帯
Term / Day / Period

秋木曜日３時限
Fall Thu 3

授業形態
Course style

学科・専攻
Department / Program

数理学科

必修・選択
Required / Selected

授業の目的　【日本語】
Goals of the Course(JPN)

授業の目的　【英語】
Goals of the Course

Introduce some basics of the representation theory of finite groups in both ordinary and modular characteristics, including basic understandings of character theoretic, module theoretic, and quiver representation theoretic approaches.

到達目標　【日本語】
Objectives of the Course(JPN))

到達目標　【英語】
Objectives of the Course

-Understand basic properties of group algebras.
-Be able to translate between representations, characters, and modules.
-Learn to calculate ordinary characters of finite groups of small orders.
-Be able to calculate with quiver-and-relations of certain block algebras, including the Brauer tree algebras, Kronecker algebra and its self-injective analogue.

授業の内容や構成
Course Content / Plan

Part I: Ordinary characteristic theory:
Representations of groups, Maschke's theorem, tensor and dual, induction and restriction, permutation representations
Basics of ordinary character theory

Part II: Modular characteristic theory:
Artin-Wedderburn theorem, Jordan-Holder theorem, radical/socle series.
Blocks, symmetricity. The group algebras of cyclic groups. Brauer tree algebras. Kronecker algebra and representation-finite groups algebras.

If time allows: Cellular algebra approach for Weyl groups.

履修条件
Course Prerequisites

Linear algebra is necessary. Basic knowledge of groups, rings, and modules.