Reprezentacije Virasorove algebre

Čeperić, Ante (2015) Reprezentacije Virasorove algebre. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

In this work, we study the Virasoro algebra and its representations. The goal of the first chapter is to introduce basic notions from the theory of Lie algebras. We construct the universal enveloping algebra, define central extensions of Lie algebra L and show their correspondence with certain bilinear functions on L. In second chapter three Lie algebras are defined: Witt, Heisenberg and Virasoro algebra, and some of their properties shown. Virasoro algebra is characterized as a universal central extension of Witt algebra. In third chapter we first show a few general results concerning representations of Virasoro algebra. Some examples of Virasoro algebra representations are given, and their properties analysed. From here, the focus is on the highest weight representations. We construct universal highest weight representations, the Verma modules, and analyse their structure. More concretely, homomorphisms between Verma modules are described, and as a corollary we get the description of submodules of Verma modules. Fourth chapter is a short exposition of the theory of vertex algebras. We build vertex algebras over Heisenberg and Virasoro algebra and show their relationship with representations of Virasoro algebra.

Item Type: Thesis (Diploma thesis)
Supervisor: Adamović, Dražen
Date: 2015
Number of Pages: 57
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 07 Oct 2015 09:13
Last Modified: 07 Oct 2015 09:13
URI: http://digre.pmf.unizg.hr/id/eprint/4132

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