Excision in Algebraic K-Theory and Karoubi's Conjecture

We prove that the property of excision in algebraic K-theory is for a Q-algebra A equivalent to the H-unitality of the latter. Our excision theorem, in particular, implies Karoubi's conjecture on the equality of algebraic and topological K-theory groups of stable C*-algebras. It also allows us...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 1990-12, Vol.87 (24), p.9582-9584
Main Authors: Suslin, Andrei A., Wodzicki, Mariusz
Format: Article
Language:English
Subjects:
Abstract algebra
Algebra
Algebraic topology
Functors
Mathematical rings
Mathematical theorems
Subalgebras
Subrings
Topological theorems
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Summary:We prove that the property of excision in algebraic K-theory is for a Q-algebra A equivalent to the H-unitality of the latter. Our excision theorem, in particular, implies Karoubi's conjecture on the equality of algebraic and topological K-theory groups of stable C*-algebras. It also allows us to identify the algebraic K-theory of the symbol map in the theory of pseudodifferential operators.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.87.24.9582