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

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

1999-06-21

arxiv.org/abs/math/9906141v1

Mathematics

Rings and Algebras

12 pages; to appear in Pacific J. Math

Scientific paper

For 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.

Affiliated with

Also associated with

No associations

Rating

$K_1$ of separative exchange rings and C*-algebras with real rank zero does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with $K_1$ of separative exchange rings and C*-algebras with real rank zero, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and $K_1$ of separative exchange rings and C*-algebras with real rank zero will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-386583