On Levi Decompositions in Finite and Infinite Dimensional Lie Algebras
(2021) In Bachelor's Theses in Mathematical Sciences MATK11 20202Mathematics (Faculty of Engineering)
Mathematics (Faculty of Sciences)
 Abstract
 In this bachelor thesis we introduce Lie algebras, and use Lie algebra cohomology to prove Levi's theorem about splitting of finite dimensional Lie algebras. We then construct the Virasoro algebra, compute its low dimensional cohomology spaces, and use this to demonstrate why Levi's theorem does not hold in the infinite dimensional case.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/9040553
 author
 Nilsson, Hannes ^{LU}
 supervisor

 Arne Meurman ^{LU}
 organization
 course
 MATK11 20202
 year
 2021
 type
 M2  Bachelor Degree
 subject
 keywords
 Lie algebra, Levi's theorem, Cohomology, Virasoro algebra
 publication/series
 Bachelor's Theses in Mathematical Sciences
 report number
 LUNFMA41072021
 ISSN
 16546229
 other publication id
 2021:K1
 language
 English
 id
 9040553
 date added to LUP
 20210322 16:29:03
 date last changed
 20210322 16:29:03
@misc{9040553, abstract = {{In this bachelor thesis we introduce Lie algebras, and use Lie algebra cohomology to prove Levi's theorem about splitting of finite dimensional Lie algebras. We then construct the Virasoro algebra, compute its low dimensional cohomology spaces, and use this to demonstrate why Levi's theorem does not hold in the infinite dimensional case.}}, author = {{Nilsson, Hannes}}, issn = {{16546229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor's Theses in Mathematical Sciences}}, title = {{On Levi Decompositions in Finite and Infinite Dimensional Lie Algebras}}, year = {{2021}}, }