Skip to main content

LUP Student Papers

LUND UNIVERSITY LIBRARIES

On Levi Decompositions in Finite and Infinite Dimensional Lie Algebras

Nilsson, Hannes LU (2021) In Bachelor's Theses in Mathematical Sciences MATK11 20202
Mathematics (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:
author
Nilsson, Hannes LU
supervisor
organization
course
MATK11 20202
year
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}},
}