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master's thesis
Liejeve algebre
2017. urn:nbn:hr:166:695397
Ćurić, Nada
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Ćurić, N. (2017). Liejeve algebre (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:695397

Ćurić, Nada. "Liejeve algebre." Master's thesis, University of Split, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:166:695397

Ćurić, Nada. "Liejeve algebre." Master's thesis, University of Split, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:166:695397

Ćurić, N. (2017). 'Liejeve algebre', Master's thesis, University of Split, Faculty of Science, accessed 18 April 2024, https://urn.nsk.hr/urn:nbn:hr:166:695397

Ćurić N. Liejeve algebre [Master's thesis]. Split: University of Split, Faculty of Science; 2017 [cited 2024 April 18] Available at: https://urn.nsk.hr/urn:nbn:hr:166:695397

N. Ćurić, "Liejeve algebre", Master's thesis, University of Split, Faculty of Science, Split, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:166:695397

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Metadata
TitleLiejeve algebre
Title (english)Lie algebras
AuthorNada Ćurić
MentorSaša Krešić Jurić (mentor)
Committee memberSaša Krešić Jurić (predsjednik povjerenstva)
Committee memberGordan Radobolja (član povjerenstva)
Committee memberTea Martinić Bilać (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2017-09-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Tema ovog rada su Liejeve algebre. U prvom poglavlju se uvodi pojam Liejevealgebre te se navode neki primjeri. Potom se definira kvocijentna Liejeva algebra i dokazuju teoremi o izomorfizmu. Definiraju se pojmovi centra, centralizatora i normalizatora Liejevih algebri kao i njihova svojstva. Na kraju poglavlja se definira adjungirana reprezentacija. Na početku drugog poglavlja se definira izvedena Liejeva algebra koja nam je potrebna kako bismo uveli pojam rješive Liejeve algebre. Na kraju poglavlja se dokazuje glavni rezultat, Liejev teorem. U trećem poglavlju se uvodi pojam nilpotentnih Liejevih algebri i kompleksifikacije realne Liejeve algebre. Zatim se definira Killingova forma, te se izvode uvjeti na formi koji su nužni i dovoljni da bi Liejeva algebra bila rješiva, odnosno poluprosta.
Abstract (english)
The subject of this paper are Lie algebras. In the first chapter we introduce the notion of Lie algebras and we give some examples. Then we define the quotient Lie algebra and weprove the isomorphism theorems. Afterwards, we define the center, centralizer and normalizer of a Lie algebra and we prove some of their properties. At the end of the chapter we define the adjoint representation. In the second chapter we define the derived algebra which is important to define solvable Lie algebra. At the end of chapter we prove the main result, Lie’s theorem. In the third chapter we introduce nilpotent Lie algebras and complexification of aLie algebra. Then we define the Killing form on a Lie algebra and derive necessary and sufficient conditions on this form for a Lie algebra to be solvable or semisimple.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:695397
Study programmeTitle: Mathematics and Computer Science; specializations in: major in teaching
Course: major in teaching
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2018-05-18 15:54:02