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master's thesis
Sistemi korijena i poluproste Liejeve algebre
2022. urn:nbn:hr:166:829426
Mandarić, Marcela
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Mandarić, M. (2022). Sistemi korijena i poluproste Liejeve algebre (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:829426

Mandarić, Marcela. "Sistemi korijena i poluproste Liejeve algebre." Master's thesis, University of Split, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:166:829426

Mandarić, Marcela. "Sistemi korijena i poluproste Liejeve algebre." Master's thesis, University of Split, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:166:829426

Mandarić, M. (2022). 'Sistemi korijena i poluproste Liejeve algebre', Master's thesis, University of Split, Faculty of Science, accessed 26 December 2024, https://urn.nsk.hr/urn:nbn:hr:166:829426

Mandarić M. Sistemi korijena i poluproste Liejeve algebre [Master's thesis]. Split: University of Split, Faculty of Science; 2022 [cited 2024 December 26] Available at: https://urn.nsk.hr/urn:nbn:hr:166:829426

M. Mandarić, "Sistemi korijena i poluproste Liejeve algebre", Master's thesis, University of Split, Faculty of Science, Split, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:166:829426

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Metadata
TitleSistemi korijena i poluproste Liejeve algebre
Title (english)Root systems and semisimple Lie algebras
AuthorMarcela Mandarić
MentorGordan Radobolja (mentor)
Committee memberGordan Radobolja (predsjednik povjerenstva)
Committee memberSaša Krešić Jurić (član povjerenstva)
Committee memberTea Martinić Bilać (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2022-09-22, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Cilj ovog rada je klasificirati konačnodimenzionalne poluproste kompleksne Liejeve algebre. U tu svrhu smo prvo uveli općeniti pojam sistema korijena, baze sistema korijena te Weylove grupe. Svakom sistemu korijena smo pridružili Cartanovu matricu i Dynkinov dijagram koji sadržavaju potrebne informacije o sistemima korijena te omogućavaju klasifikaciju svih sistema korijena. Nadalje smo za konačnodimenzionalnu poluprostu kompleksnu Liejevu algebru definirali Cartanovu podalgebru, Cartanovu dekompoziciju te korijene što nam je omogućilo da primjenimo klasifikacijski teorem za sisteme korijena na Liejeve algebre. To je bilo moguće zbog bijektivne veze izmedu konačnodimenzionalne poluproste kompleksne Liejeve algebre i pripadnog sistema korijena. Prvo smo se sveli na proste i zaključili smo da postoje četiri beskonačne familije takvih algebri i pet iznimaka. Kako su poluproste direktna suma prostih time je bila dovršena klasifikacija i poluprostih.
Abstract (english)
Goal of this paper is to classify finitedimensional semisimple complex Lie algebras. In order to do that we firstly introduce root systems in general, bases of a root system and the Weyl group. We joined a Cartan matrix and Dynkin diagram to each root system which contain important information about the root system and enable the classification of the root systems. Furthermore, we defined Cartan subalgebra, Cartan decomposition and roots for finitedimensional complex semisimple Lie algebra which enabled us to apply classification theorem for root systems on Lie algebras. It was possible because of bijective relation between finitedimensional semisimple complex Lie algebras and it’s root system. We firstly explored simple Lie algebras and concluded that there are four infinite families and five exeptional. Since those that are semisimple are a direct sum of simple Lie algebras, classification of those that are semisimple is over by classifying simple ones.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:829426
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching, major in statistics and computing
Course: major in pure mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-12-15 13:53:55