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The smallestC*-algebra for canonical commutations relations

1973; Springer Science+Business Media; Volume: 32; Issue: 3 Linguagem: Inglês

10.1007/bf01645594

1432-0916

J. Manuceau, M. Sirugue, D. Testard, A. Verbeure,

Advanced Algebra and Geometry

We consider theC*-algebras which contain the Weyl operators when the symplectic form which defines the C.C.R. is possibly degenerate. We prove that the C.C.R. are all obtained as a quotient of a universalC*-algebra by some of its ideals, and we characterize all these ideals.