Lifting Projective Representations



We investigate lifting projective representations in matrix Lie groups to unitary representations. After establishing preliminary notions, we discuss finite- and infinite-dimensional representations of matrix Lie groups, emphasizing the relationship between SU(2) and SO(3) and thus providing applications in quantum physics. The application of cohomological methods in studying the lifting of projective representations is then highlighted, along with the concept of one-dimensional central extensions. We then outline a proof of Bargmann’s theorem, which addresses the existence of lifts for possibly infinite-dimensional projective representations of Lie groups whose second group cohomology vanishes.


Attribute NameValues
Alternate Title
  • Lifting Projective Representations and Bargmann’s Theorem

  • Greyson C. Wesley

  • Greyson C. Wesley

Journal or Work Title
  • Senior Honors Thesis

First Page
  • 1

Last Page
  • 35

Number of Pages
  • 36

  • Group Cohomology

  • Lie Theory

  • Representation Theory

  • Smooth Manifolds

  • University of Notre Dame

Date Created
  • 2023-04-15

  • English

Departments and Units
Record Visibility Public
Content License

Digital Object Identifier


This DOI is the best way to cite this article.


Please Note: You may encounter a delay before a download begins. Large or infrequently accessed files can take several minutes to retrieve from our archival storage system.