|
A note on  -operations in orthogonal K-theory
Author(s):
Mohamed
Elhamdadi
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1-4.
MSC (1991):
Primary 19G38, 11E57
Posted:
September 9, 1999
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
In Comment. Math. Helv. 55 (1980), 233-254, Kratzer defined Lambda operations on classical algebraic K-theory by using exterior powers of representations and a splitting principle (R. G. Swan, Proc. Sympos. in Pure Math. 21 (1971), 155-159). Because hyperbolic forms are not stable under exterior powers, we instead use a larger class of symmetric bilinear forms to define the operation of exterior powers on the classifying space of the orthogonal K-theory.
References:
- 1.
- A. Bak, K-theory of forms. Annals of Math. Studies, Princ. Univ. Press 1980. MR 84m:10012
- 2.
- M. Elhamdadi, Sur les Lambda-opérations et la L-théorie, Thèse de Doctorat de l'université de Nice-Sophia Antipolis (1996).
- 3.
- H. Hiller, -rings and algebraic K-theory, J. Pure Appl. Algebra 20 (1981), 241-266. MR 82e:18016
- 4.
- M. Karoubi, Théorie de Quillen et homologie du groupe orthogonal, Ann. of Math. 112 (1980), 207-257. MR 82h:18011
- 5.
- M. A. Knus, Quadratic and Hermitian Forms over Rings, Grundlehren der math. Wissenschaften 294. Springer, Berlin 1991. MR 92i:11039
- 6.
- Ch. Kratzer, Lambda-structures en K-théorie algébrique, Comment. Math. Helv. 55 (1980), 233-254. MR 81m:18011
- 7.
- J. L. Loday, K-théorie algébrique et représentations de groupes, Ann. Sci. Ecole Norm. Sup. 9 (1976), 309-377. MR 56:5686
- 8.
- A. Roy, Cancellation of quadratic forms over commutative rings, J. Algebra 10 (1968), 286-298. MR 38:172
- 9.
- C. Soulé, Opérations en K-théorie algébrique, Can. J. Math. vol. XXXVII, N 3 (1985), 488-550. MR 87b:18013
- 10.
- R. G. Swan, A Splitting Principle in Algebraic K-theory, Proc. Symp. in Pure Math. 21 (1971), 155-159. MR 47:5079
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
19G38, 11E57
Retrieve articles in all Journals with MSC
(1991):
19G38, 11E57
Additional Information:
Mohamed
Elhamdadi
Affiliation:
Department of Mathematics, University of South Florida, 4202 East Fowler Ave., PHY 114, Tampa, Florida 33620-5700
Email:
emohamed@math.usf.edu
DOI:
10.1090/S0002-9939-99-05376-9
PII:
S 0002-9939(99)05376-9
Received by editor(s):
January 23, 1998
Posted:
September 9, 1999
Communicated by:
Ralph Cohen
Copyright of article:
Copyright
1999,
American Mathematical Society
|
Comments: webmaster@ams.org