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

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dc.creatorAguilar, M. A.
dc.creatorSocolovsky, M.
dc.date1999-11-23
dc.date.accessioned2026-07-07T04:33:06Z
dc.date.available2026-07-07T04:33:06Z
dc.descriptionUsing fibre bundle theory we construct the universal covering group of U(n), $\tilde{U}(n)$, and show that $\tilde{U}(n)$ 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.
dc.description18 pages, Plain TeX
dc.identifierhttps://arxiv.org/abs/math-ph/9911028
dc.identifierhttp://arxiv.org/abs/math-ph/9911028
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58447
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.titleThe Universal Covering Group of U(n) and Projective Representations
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