The Universal Covering Group of U(n) and Projective Representations
نویسنده
چکیده
Using fibre bundle theory we construct the universal covering group of U(n), Ũ(n), and show that Ũ(n) is isomorphic to the semidirect product SU(n)©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) ©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) ©s R. For completeness, we discuss the topological and group theoretical relations between U(n), SU(n), U(1) and Zn.
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