Određivanje podmodula za Liejeve algebre tipa A i C

undergraduate thesis

• Title (english): Determination of Submodules for Lie Algebras of Type A and C
• Author: Mario Tropčić
• Mentor: Domagoj Kovačević (mentor)
• Committee member: Domagoj Kovačević (predsjednik povjerenstva)
• Committee member: Mario Osvin Pavčević (član povjerenstva)
• Committee member: Tomislav Šikić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2021-06-17, 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: Liejeve algebre; moduli; podmoduli; Cartanova podalgebra; korijeni; težine; Freudenthalova formula
• Keywords (english): Lie algebras; modules; submodules; Cartan subalgebra; roots; weights; Freudenthal's formula
• Language: croatian
• URN:NBN: urn:nbn:hr:168:123285
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2023-01-14 21:53:25