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undergraduate thesis
Određivanje podmodula za Liejeve algebre tipa A i C
Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing, 2021. urn:nbn:hr:168:123285
Tropčić, Mario
University of Zagreb
Faculty of Electrical Engineering and Computing

Institutional repository: FER Repository

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Tropčić, M. (2021). Određivanje podmodula za Liejeve algebre tipa A i C (Undergraduate thesis). Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing. Retrieved from https://urn.nsk.hr/urn:nbn:hr:168:123285

Tropčić, Mario. "Određivanje podmodula za Liejeve algebre tipa A i C." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2021. https://urn.nsk.hr/urn:nbn:hr:168:123285

Tropčić, Mario. "Određivanje podmodula za Liejeve algebre tipa A i C." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2021. https://urn.nsk.hr/urn:nbn:hr:168:123285

Tropčić, M. (2021). 'Određivanje podmodula za Liejeve algebre tipa A i C', Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, accessed 04 December 2024, https://urn.nsk.hr/urn:nbn:hr:168:123285

Tropčić M. Određivanje podmodula za Liejeve algebre tipa A i C [Undergraduate thesis]. Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing; 2021 [cited 2024 December 04] Available at: https://urn.nsk.hr/urn:nbn:hr:168:123285

M. Tropčić, "Određivanje podmodula za Liejeve algebre tipa A i C", Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:168:123285

Metadata
TitleOdređivanje podmodula za Liejeve algebre tipa A i C
Title (english)Determination of Submodules for Lie Algebras of Type A and C
AuthorMario Tropčić
MentorDomagoj Kovačević (mentor)
Committee memberDomagoj Kovačević (predsjednik povjerenstva)
Committee memberMario Osvin Pavčević (član povjerenstva)
Committee memberTomislav Šikić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Electrical Engineering and Computing
Zagreb
Defense date and country2021-06-17, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Computing
Abstract
Liejeva algebra 𝖌 je vektorski prostor nad poljem F na kojem je definirana bilinearna operacija zvana Liejeva zagrada, koja zadovoljava Jacobijev identitet. Cartanova podalgebra 𝖍 je nilipotentna podalgebra od 𝖌 koja je jednaka svom normalizatoru. Cartanove podalgebre možemo podjeliti u četiri famlije podalgebri (An, Bn, Cn, Dn), svaka sa svojim pripadnim korijenskim sustavom čiji korijeni tvore realni vektorski potprostor. Modul je vektorski prostor zajedno s djelovanjem Liejeve algebre na njemu te se svaki modul može prikazati kao kompozicija podmodula. Napomenimo da su podmoduli zapravo moduli za djelovanje podalgebre dane algebre. Dakle dekompoziciju modula računamo kao sumu podmodula koji su zapravo moduli određene podalgebre.
Abstract (english)
Lie algebra 𝖌 is a vector space with an operation called the Lie bracket, that satisfies the Jacobi identity. Cartan subalgebra is a nilipotent subalgebra 𝖍 of Lie algebra 𝖌 that is self–normalising. Cartan's subalgebras can be divided into four families of subalgebras (An, Bn, Cn, Dn), each with its own unique root system whose roots form real vector subspace. A modul is a vector space together with the action of Lie algebra on it and each module can be represented as a composition of submoduls. Note that submodules are actually modules for the action of a subalgebra of a given algebra. Decomposition of moduls is calculated as the sum of submoduls which are actually moduls of a certain subalgebra.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:168:123285
Study programmeTitle: Computing
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
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File originBorn digital
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Created on2023-01-14 21:53:25