Reprezentacije kompaktnih Liejevih grupa

Pantaler, Mateja (2015) Reprezentacije kompaktnih Liejevih grupa. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

As an introductory part, the paper begins with definitions of basic notions that we often meet with in mathematics, and that are important in the sequel. Definitions of basic notions are followed by the introduction into theory of representations, where notions like group representations, faithful representations, equivalence of representations, irreducible representations, reducible representations and completely reducible representations are defined. Similar definitions are used also in the case when the group is compact. Also, the notions related to representations of compact groups are defined. Peter-Weyl theorem, as well as consequences of this theorem, are presented. Before the theorem is proven, the terms used in the proof are defined. The definitions of Lie algebras and Lie groups are given and some of examples of Lie groups are brought up. It is proven that each compact Lie group has a faithful representation. In the final chapter the character of an irreducible representation is defined and the important results that Weyl reached are given: Weyl integration formula, Weyl character and dimension formulae.

Item Type: Thesis (Diploma thesis)
Supervisor: Pandžić, Pavle
Date: 2015
Number of Pages: 32
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 23 Oct 2015 11:03
Last Modified: 23 Oct 2015 11:03
URI: http://digre.pmf.unizg.hr/id/eprint/4303

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