The Universal Covering Group of U(n) and Projective Representations

1999/11/23 by Marcelo Aguilar, M. A. Aguilar, Aguilar, M. A. +2
Mathematics · Medicine · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Ophthalmology and Eye Disorders #hep-th #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/9911028

18 pages, Plain TeX

arxiv created 1999/11/23 · openalex publication_date 1999/11/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using fibre bundle theory we construct the universal covering group of U(n), U(n), and show that U(n) is isomorphic to the semidirect product SU(n)\bigcirc \scriptstyle s R. We give a bijection between the set of projective representations of U(n) and the set of equivalence classes of certain unitary representations of SU(n)\bigcirc \scriptstyle s R. Applying Bargmann's theorem, we give explicit expressions for the liftings of projective representations of U(n) to unitary representations of SU(n)\bigcirc \scriptstyle s R. For completeness, we discuss the topological and group theoretical relations between U(n), SU(n), U(1) and Z_n.

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