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master's thesis
Reprezentacije konačnih grupa
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:378845
Perica, Fran
University of Zagreb
Faculty of Science
Department of Mathematics

Cite this document

Perica, F. (2022). Reprezentacije konačnih grupa (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:378845

Perica, Fran. "Reprezentacije konačnih grupa." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:378845

Perica, Fran. "Reprezentacije konačnih grupa." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:378845

Perica, F. (2022). 'Reprezentacije konačnih grupa', Master's thesis, University of Zagreb, Faculty of Science, accessed 15 January 2025, https://urn.nsk.hr/urn:nbn:hr:217:378845

Perica F. Reprezentacije konačnih grupa [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2025 January 15] Available at: https://urn.nsk.hr/urn:nbn:hr:217:378845

F. Perica, "Reprezentacije konačnih grupa", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:378845

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Metadata
TitleReprezentacije konačnih grupa
Title (english)Representations of finite groups
AuthorFran Perica
MentorPavle Pandžić (mentor)
Committee memberPavle Pandžić (predsjednik povjerenstva)
Committee memberPetar Žugec (član povjerenstva)
Committee memberFilip Najman (član povjerenstva)
Committee memberMea Bombardelli (član povjerenstva)
Committee memberMarko Tomislav Cvitaš (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-09-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract
Prvo poglavlje je namijenjeno kao dobar uvod u teoriju reprezentacija jer se kreće samo s bazičnim znanjem linearne algebre. Uvode se osnovne definicije i brzo se prelazi na primjere odnosno na reprezentacije Abelove grupe \(\mathfrak{G}_{3}\). Zatim se detaljnije uvode karakteri reprezentacija koji su od velike važnosti jer karakter neke reprezentacije govori dosta o samoj reprezentaciji. Uz uvod u projekcijske formule, također je i detaljno pokazan postupak pronalaska tablice karaktera za određene reprezentacije i to je napravljeno za \(\mathfrak{G}_{4}\). Zatim imamo još dobrih primjera kao što su tablice karaktera od \(\mathfrak{U}_{5}\) i posebito \(\mathfrak{G}_{5}\) koji nam dobro pokazuje kako evoluira tablica karaktera kada mijenjamo broj elemenata u nekoj permutacijskoj grupi. Završava se s kratkim uvodima u grupnu algebru, realnim i induciranim reprezentacijama.
Abstract (english)
The first chapter is intended as a gentle introduction to the theory of representations because it only assumes basic knowledge of linear algebra. Basic definitions are introduced followed by an example where we explore representations of the Abelian group \(\mathfrak{G}_{3}\). Next concept is the characters of representations which are of great importance in the theory as they give a lot of information about the representation itself. Along with introducing projection formulas here we show how to construct character tables for different representations, in this case on the group \(\mathfrak{G}_{4}\). What follows is a pair of good examples as we construct more character tables, for \(\mathfrak{U}_{5}\) and more importantly for \(\mathfrak{G}_{5}\) where we can see how the tables change when we add elements to a permutation group. In the end there is a short introduction to group algebra, real and induced representations.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:378845
Study programmeTitle: Mathematics and Physics Education; specializations in: Mathematics and Physics Education
Course: Mathematics and Physics Education
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije matematike i fizike (magistar/magistra edukacije matematike i fizike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
RepositoryRepository of the Faculty of Science
Created on2022-11-04 12:46:37

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