Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Adjoint action of a finite loop space

Author: Norio Iwase
Journal: Proc. Amer. Math. Soc. 125 (1997), 2753-2757
MSC (1991): Primary 55P45, 55Q25; Secondary 55N20
MathSciNet review: 1401745
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Adjoint actions of compact simply connected Lie groups are studied by A. Kono and K. Kozima based on the series of studies on the classification of compact Lie groups and their cohomologies. At odd primes, there is a simpler homotopy theoretic approach that will prove the results of Kono and Kozima for any finite loop spaces. However, there are some technical difficulties at the prime 2.

References [Enhancements On Off] (What's this?)

  • 1. W. Browder, On differential Hopf algebras, Trans. Amer. Math. Soc. 107 (1963), 153-176. MR 26:3061
  • 2. A. Clark, Homotopy commutativity and the Moore spectral sequence, Pacific. J. Math. 15 (1965), 65-74. MR 31:1679
  • 3. A.L. Cook and M.C. Crabb, Fibrewise Hopf structures on sphere-bundles, J. London Math. Soc. 48 (1993), 365-384. MR 94d:55021
  • 4. R. Kane, Primitivity and finite H-spaces, Q. J. Math. Oxford 3 (1975), 185-197. MR 52:9220
  • 5. K. Kono and K. Kozima, The adjoint action of a Lie group on the space of loops, J. Math. Soc. Japan 45 (1993), 495-509. MR 94h:57053
  • 6. J.P. Lin, Torsion in H-spaces II, Ann. Math. 107 (1978), 41-88. MR 58:7619
  • 7. J. Milnor and J.C. Moore, On the structure of Hopf Algebras, Ann. Math. 81 (1965), 211-264. MR 30:4259
  • 8. J.C. Moore, La Suspension, Seminar H. Cartan 12 (1959/60), expose 6.
  • 9. A. Zabrodsky, Implications in the cohomology of H-space, Illinois J. Math. 16 (1971), 363-375. MR 41:6217

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 55P45, 55Q25, 55N20

Retrieve articles in all journals with MSC (1991): 55P45, 55Q25, 55N20

Additional Information

Norio Iwase
Affiliation: Graduate School of Mathematics Ropponmatsu, Kyushu University, Ropponmatsu 4-2-1, Fukuoka 810, Japan

Keywords: Loop group, loop space
Received by editor(s): November 21, 1995
Received by editor(s) in revised form: March 21, 1996
Additional Notes: This research was supported by Grant-in-Aid for Scientists (C)08640125 from the Ministry of Education, Science and Culture of Japan.
Dedicated: Dedicated to the memory of Kiyono Iwase
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society