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Lie-teori och nästan kommutativa fält
Örebro University, School of Science and Technology.
2016 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Lie theory and almost commutative vector fields (English)
Abstract [sv]

Vi ger en överskådlig introduktion till mångfalder, Lie-grupper och deras

associerade Lie-algebror. En karaktärisering av Lie-parentesen som naturligt

kopplar ihop de vanligast förekommande karaktäriseringarna presenteras

(sats 4.4.1). Vi använder idéer från Riemanngeometrin för att inleda

en undersökning av vad det betyder för vektorfält på Lie-grupper att vara

_mer eller mindre kommutativa_. Vi presenterar ett mått av kommutativitet,

diskuterar dess egenskaper och avslutar med några förslag på framtida

undersökningar.

Abstract [en]

We give a comprehensive introduction to manifolds, Lie groups, and their

associated Lie algebras. A characterization of the Lie bracket which connects

the most commonly seen characterizations in a canonical fashion is presented

(thm. 4.4.1). We make use of ideas from Riemannian geometry to begin an

investigation of what it means for vector elds on Lie groups to be more

or less commutative. We present a measure of commutativity, discuss its

properties, and close with a few suggestions for future work.

Place, publisher, year, edition, pages
2016. , 66 p.
Keyword [sv]
Lie-grupp, Lie-algebra, vektorfält, kommutativitet, Riemanngeometri.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-50584OAI: oai:DiVA.org:oru-50584DiVA: diva2:933841
Subject / course
Mathematics
Supervisors
Examiners
Available from: 2016-06-07 Created: 2016-06-07 Last updated: 2017-10-17Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • asciidoc
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