Abstract
Using fiber 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) ∝.We give a bijection between the set of projective representations of U(n) and theset of equivalence classes of certain unitary representations of SU(n) ∝.Applying Bargmann's theorem, we give explicit expressions for the liftings ofprojective representations of U(n) to unitary representations of SU(n) ∝. Forcompleteness, we discuss the topological and group theoretic relations betweenU(n), SU(n), U(t), and Z n .
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Aguilar, M.A., Socolovsky, M. Universal Covering Group of U(n) and Projective Representations. International Journal of Theoretical Physics 39, 997–1013 (2000). https://doi.org/10.1023/A:1003694206391
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DOI: https://doi.org/10.1023/A:1003694206391