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undergraduate thesis
Vizualizacija kombinatornih baza standardnih modula simplektičkih afinih Lievih algebri
Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing, 2020. urn:nbn:hr:168:666491
Špiljak, Dominik
University of Zagreb
Faculty of Electrical Engineering and Computing

Institutional repository: FER Repository

Cite this document

Špiljak, D. (2020). Vizualizacija kombinatornih baza standardnih modula simplektičkih afinih Lievih algebri (Undergraduate thesis). Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing. Retrieved from https://urn.nsk.hr/urn:nbn:hr:168:666491

Špiljak, Dominik. "Vizualizacija kombinatornih baza standardnih modula simplektičkih afinih Lievih algebri." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2020. https://urn.nsk.hr/urn:nbn:hr:168:666491

Špiljak, Dominik. "Vizualizacija kombinatornih baza standardnih modula simplektičkih afinih Lievih algebri." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2020. https://urn.nsk.hr/urn:nbn:hr:168:666491

Špiljak, D. (2020). 'Vizualizacija kombinatornih baza standardnih modula simplektičkih afinih Lievih algebri', Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, accessed 17 July 2024, https://urn.nsk.hr/urn:nbn:hr:168:666491

Špiljak D. Vizualizacija kombinatornih baza standardnih modula simplektičkih afinih Lievih algebri [Undergraduate thesis]. Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing; 2020 [cited 2024 July 17] Available at: https://urn.nsk.hr/urn:nbn:hr:168:666491

D. Špiljak, "Vizualizacija kombinatornih baza standardnih modula simplektičkih afinih Lievih algebri", Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:168:666491

Metadata
TitleVizualizacija kombinatornih baza standardnih modula simplektičkih afinih Lievih algebri
Title (english)Visualization of combinatorial bases for standard modules of symplectic affine Lie algebras
AuthorDominik Špiljak
MentorTomislav Šikić (mentor)
Committee memberTomislav Šikić (predsjednik povjerenstva)
Committee memberDomagoj Kovačević (član povjerenstva)
Committee memberMate Puljiz (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Electrical Engineering and Computing
Zagreb
Defense date and country2020-07-08, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Computing
Abstract
U radu se proučavaju osnovni koncepti Liejeve algebre – posebno simplektičke Liejeve algebre te vizualizacije kombinatornih baza. Na početku kao motivacijsko poglavlje, dane su neke od primjena Liejeve algebre u matematici, fizici i računarskoj znanosti. Objašnjene su definicija te osnovna svojstva Liejeve algebre, definirani su pojmovi izomorfizma i podalgebre. Objašnjen je pojam linearne Liejeve algebre uz pojam glavne linearne algebre, definirana je jedna od linearnih Liejevih algebra, specijalna Liejeva algebra 𝖘𝖑(𝑛,ℂ). Objašnjen je pojam bilinearne forme i antidijagonalizacijskog teorema. Zatim je definirana i objašnjena simplektička Liejeva algebra 𝖘𝖕(2𝑙,𝔽). U drugom poglavlju, objašnjen je način vizualizacije baza simplektičke Liejeve algebre uz pomoć Cartanove dekompozicije i objašnjena je programska izvedba vizualizacije baza simplektičke Liejeve algebre.
Abstract (english)
The paper studies the basic concepts of Lie algebra - especially sympletic Lie algebras and visualizations of combinatorial bases. Initially as a motivational chapter, some of the applications of Lie algebra in mathematics, physics, and computer science are given. The definition and basic properties of Lie algebra are explained, the concepts of isomorphism and subalgebra are defined. The notion of linear Lie algebra is explained along with the notion of general linear algebra, one of the linear Lie algebras is defined, the simple Lie algebra\ \mathbf{sl}(n,\ \mathbb{C}). The notion of bilinear form and antidiagonalization theorem is explained. Then, the symplectic Lie algebra \mathbf{sp}(2l,\ \mathbb{F}) is defined and explained. In the second chapter, the way of visualization of bases of symplectic Lie algebra is explained using Cartan decomposition and the program implementation of visualization of bases of symplectic Lie algebra is explained.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:168:666491
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)
Type of resourceText
File originBorn digital
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Created on2023-01-14 10:05:03