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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on $\lambda$-operations in orthogonal K-theory
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by Mohamed Elhamdadi
Proc. Amer. Math. Soc. 128 (2000), 1-4
DOI: https://doi.org/10.1090/S0002-9939-99-05376-9
Published electronically: September 9, 1999
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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
  • Anthony Bak, $K$-theory of forms, Annals of Mathematics Studies, No. 98, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1981. MR 632404
  • M. Elhamdadi, Sur les Lambda-opĂ©rations et la L-thĂ©orie, ThĂšse de Doctorat de l’universitĂ© de Nice-Sophia Antipolis (1996).
  • Howard L. Hiller, $\lambda$-rings and algebraic $K$-theory, J. Pure Appl. Algebra 20 (1981), no. 3, 241–266. MR 604319, DOI 10.1016/0022-4049(81)90062-1
  • Max Karoubi, ThĂ©orie de Quillen et homologie du groupe orthogonal, Ann. of Math. (2) 112 (1980), no. 2, 207–257 (French). MR 592291, DOI 10.2307/1971326
  • Max-Albert Knus, Quadratic and Hermitian forms over rings, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 294, Springer-Verlag, Berlin, 1991. With a foreword by I. Bertuccioni. MR 1096299, DOI 10.1007/978-3-642-75401-2
  • Ch. Kratzer, $\lambda$-structure en $K$-thĂ©orie algĂ©brique, Comment. Math. Helv. 55 (1980), no. 2, 233–254 (French). MR 576604, DOI 10.1007/BF02566684
  • Jean-Louis Loday, $K$-thĂ©orie algĂ©brique et reprĂ©sentations de groupes, Ann. Sci. École Norm. Sup. (4) 9 (1976), no. 3, 309–377 (French). MR 447373
  • Amit Roy, Cancellation of quadratic form over commutative rings, J. Algebra 10 (1968), 286–298. MR 231844, DOI 10.1016/0021-8693(68)90080-X
  • Christophe SoulĂ©, OpĂ©rations en $K$-thĂ©orie algĂ©brique, Canad. J. Math. 37 (1985), no. 3, 488–550 (French). MR 787114, DOI 10.4153/CJM-1985-029-x
  • Richard G. Swan, A splitting principle in algebraic $K$-theory, Representation theory of finite groups and related topics (Proc. Sympos. Pure Math., Vol. XXI, Univ. Wisconsin, Madison, Wis., 1970) Amer. Math. Soc., Providence, R.I., 1971, pp. 155–159. MR 0316532
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Bibliographic Information
  • Mohamed Elhamdadi
  • Affiliation: Department of Mathematics, University of South Florida, 4202 East Fowler Ave., PHY 114, Tampa, Florida 33620-5700
  • MR Author ID: 643744
  • Email: emohamed@math.usf.edu
  • Received by editor(s): January 23, 1998
  • Published electronically: September 9, 1999
  • Communicated by: Ralph Cohen
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 128 (2000), 1-4
  • MSC (1991): Primary 19G38, 11E57
  • DOI: https://doi.org/10.1090/S0002-9939-99-05376-9
  • MathSciNet review: 1670434