| Title | Beskonačnodimenzionalne Liejeve algebre |
| Author | Ivana Vukorepa |
| Mentor(s) | Gordan Radobolja (thesis advisor)
|
| Abstract | U ovom radu proučavamo Wittovu, Heisenbergovu i Virasorovu algebru. U prvom poglavlju bavimo se osnovnim rezultatima iz teorije Liejevih algebri i reprezentacija, a potom definiramo centralna proširenja Liejevih algebri i do kazujemo neke rezultate vezane za njih. U drugom poglavlju definiramo Wittovu algebru i Virasorovu kao centralno proširenje Wittove. Zatim uvodimo pojam težinske reprezentacije i proučavamo neke reprezentacije tog tipa (Vα,β i oscilatorska reprezentacija). Nadalje, definiramo reprezentacije najveće težine i Vermaove reprezentacije i istražujemo neka njihova svojstva. |
| Keywords | Virasoro algebra representation theory weight representations Verma representations |
| Parallel title (English) | Infinite dimensional Lie algebras |
| Committee Members | Gordan Radobolja (committee chairperson)
Tea Martinić Bilać (committee member)
Dino Peran (committee member)
|
| Granter | University of Split
University of Split, Faculty of science |
| Lower level organizational units | Department of Mathematics |
| Place | Split |
| State | Croatia |
| Scientific field, discipline, subdiscipline | NATURAL SCIENCES
Mathematics
|
| Study programme type | university |
| Study level | graduate |
| Study programme | Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching |
| Study specialization | major in pure mathematics |
| Academic title abbreviation | mag. math. |
| Genre | master's thesis |
| Language | Croatian |
| Defense date | 2017-07-04 |
| Parallel abstract (English) | In this master’s thesis we study Witt, Heisenberg and Virasoro algebra. In first chapter we give some basic results from the Lie algebras and represen tation theory, and then we define Lie algebra central extensions and prove some results concerning this. In second chapter we define Witt algebra and Virasoro algebra as central extension of Witt algebra. Then we consider we ight representations and study some representations of such type (Vα,β and oscillator representation). Furthermore, we define highest weight representa tions and Verma representations and study some of their properties. |
| Parallel keywords (Croatian) | Virasorova algebra teorija reprezentacija težinske reprezentacije Vermaove reprezentacije |
| Resource type | text |
| Access condition | Access restricted to students and staff of home institution |
| Terms of use |  |
| URN:NBN | https://urn.nsk.hr/urn:nbn:hr:166:523178 |
