From Wikipedia, the free encyclopedia
Theorem connecting algebraic and topological K-theories on C* algebras
In
mathematics, the Karoubi conjecture is a conjecture by
Max Karoubi (
1979) that the algebraic and topological
K-theories coincide on
C* algebras spatially tensored with the algebra of compact operators. It was proved by
Andrei Suslin and
Mariusz Wodzicki (
1990, theorem 6,
1992).
-
Karoubi, Max (1979), "K-théorie algébrique de certaines algèbres d'opérateurs", in Harpe, Pierre de la (ed.), Algèbres d'opérateurs (Sém., Les Plans-sur-Bex, 1978),
Lecture Notes in Mathematics, vol. 725, Berlin, New York:
Springer-Verlag, pp. 254–290,
doi:
10.1007/BFb0062621,
ISBN
978-3-540-09512-5,
MR
0548119
-
Suslin, Andrei A.;
Wodzicki, Mariusz (1990), "Excision in algebraic K-theory and Karoubi's conjecture",
Proceedings of the National Academy of Sciences of the United States of America, 87 (24): 9582–9584,
Bibcode:
1990PNAS...87.9582S,
doi:
10.1073/pnas.87.24.9582,
ISSN
0027-8424,
JSTOR
2356456,
MR
1081504,
PMC
55216,
PMID
11607130
-
Suslin, Andrei A.;
Wodzicki, Mariusz (1992), "Excision in algebraic K-theory",
Annals of Mathematics, Second Series, 136 (1): 51–122,
doi:
10.2307/2946546,
ISSN
0003-486X,
JSTOR
2946546,
MR
1173926