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dbnary-eng:__ws_1_abelian__Adjective__1
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(mathematics) Of an algebraic structure, having a commutative defining operation. [Mid 19th century.]
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The interesting aspect here is that U3 is irreducible, even though all irreps over the complexes are one-dimensional because ℤ4 is abelian.
dcterms:bibliographicCitation
1996, Barry Simon, Representations of Finite and Compact Groups, page 50: