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Equivalence bimodule between non-commutative tori

Sei-Qwon Oh, Chun-Gil Park (2003)

Czechoslovak Mathematical Journal

The non-commutative torus C * ( n , ω ) is realized as the C * -algebra of sections of a locally trivial C * -algebra bundle over S ω ^ with fibres isomorphic to C * ( n / S ω , ω 1 ) for a totally skew multiplier ω 1 on n / S ω . D. Poguntke [9] proved that A ω is stably isomorphic to C ( S ω ^ ) C * ( n / S ω , ω 1 ) C ( S ω ^ ) A ϕ M k l ( ) for a simple non-commutative torus A ϕ and an integer k l . It is well-known that a stable isomorphism of two separable C * -algebras is equivalent to the existence of equivalence bimodule between them. We construct an A ω - C ( S ω ^ ) A ϕ -equivalence bimodule.

Symplectic groups are N-determined 2-compact groups

Aleš Vavpetič, Antonio Viruel (2006)

Fundamenta Mathematicae

We show that for n ≥ 3 the symplectic group Sp(n) is as a 2-compact group determined up to isomorphism by the isomorphism type of its maximal torus normalizer. This allows us to determine the integral homotopy type of Sp(n) among connected finite loop spaces with maximal torus.

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