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/student-papers/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
- LUNFMA-4107-2021
- ISSN
- 1654-6229
- other publication id
- 2021:K1
- language
- English
- id
- 9040553
- date added to LUP
- 2021-03-22 16:29:03
- date last changed
- 2021-03-22 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 = {{1654-6229}}, 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}}, }