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

M.A. Aguilar; M. Socolovsky

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

M.A. Aguilar, M. Socolovsky

Mathematical Physics · Submitted 23 Nov 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Using 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.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,786 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.07 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Using 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.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Using 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.	contribution 0.63	0.95	0.45	asserted 1.00
s1	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.	result 0.83	0.94	0.42	asserted 1.00
s2	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.	contribution 0.54	0.93	0.16	asserted 1.00
s3	For completeness, we discuss the topological and group theoretical relations between U(n), SU(n), U(1) and Z_n.	background 0.68	0.67	0.03	asserted 0.61

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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T body sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Using 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.

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3 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 2 sentences without a confident label

Cites it as background 3 papers

[ref] of the manifold $ℳ_$ [ref] .

Finite-temperature operator basis on $\mathbb{R}^3 \times S^1$ for SMEFT · Vector fields: spin-1 · 0.87
On the other hand, projective Reps of groups were less known to physicists [ref] .

Irreducible Projective Representations and Their Physical Applications · Introduction · 0.99
The first author also thanks Siyuan Chen for bringing [ref] to his mind and Jake Fillman for useful suggestions.

The fibered rotation number for ergodic symplectic cocycles and its applications: I. Gap Labelling Theorem · Interval spectrum · 0.83

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