K<inf>1</inf> of separative exchange rings and C*-algebras with real rank zero

P. Ara, K. R. Goodearl, K. C. O'Meara, R. Raphael

Research output: Contribution to journalArticleResearchpeer-review

25 Citations (Scopus)


For any (unital) exchange ring R whose finitely generated projective modules satisfy the separative cancellation property (A ⊕ A ≅ A ⊕ B ≅ B ⊕ B ⇒ A ≅ B), it is shown that all invertible square matrices over R can be diagonalized by elementary row and column operations. Consequently, the natural homomorphism GL1(R) → K1(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 K1(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.
Original languageEnglish
Pages (from-to)261-275
JournalPacific Journal of Mathematics
Issue number2
Publication statusPublished - 1 Jan 2000

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