$K_1$ of separative exchange rings and C*-algebras with real rank zero

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dc.creatorAra, P.
dc.creatorGoodearl, K. R.
dc.creatorO'Meara, K. C.
dc.creatorRaphael, R.
dc.date1999-06-21
dc.date.accessioned2026-07-07T05:29:35Z
dc.date.available2026-07-07T05:29:35Z
dc.descriptionFor any (unital) exchange ring $R$ whose finitely generated projective modules satisfy the separative cancellation property ($A\oplus A\cong A\oplus B\cong B\oplus B$ implies $A\cong B$), it is shown that all invertible square matrices over $R$ can be diagonalized by elementary row and column operations. Consequently, the natural homomorphism $GL_1(R) \to K_1(R)$ is surjective. In combination with a result of Huaxin Lin, it follows that for any separative, unital C*-algebra $A$ with real rank zero, the topological $K_1(A)$ is naturally isomorphic to the unitary group $U(A)$ modulo the connected component of the identity. This verifies, in the separative case, a conjecture of Shuang Zhang.
dc.description12 pages; to appear in Pacific J. Math
dc.identifierhttps://arxiv.org/abs/math/9906141
dc.identifierhttp://arxiv.org/abs/math/9906141
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78696
dc.subjectRings and Algebras
dc.subjectOperator Algebras
dc.subject15A33, 16E50, 19B14, 46L80
dc.title$K_1$ of separative exchange rings and C*-algebras with real rank zero
dc.typetext

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