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Primitive Generators for Algebras

Published online by Cambridge University Press:  20 November 2018

Stanley O. Kochman
Stanley O. Kochman*
Affiliation:
The University of Western Ontario, London, Ontario
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Let H be a graded commutative algebra with a nice set of algebra generators. Let H also be a comodule over a Hopf algebra A. In Section 2 we give conditions under which certain of these generators of H can be rechosen to be primitive. In addition we give explicit formulas expressing these primitive generators in terms of the original set of generators.

In Section 3 we apply the theory of Section 2 to the mod p homology of the Thorn spectra MO, MU and MSp. In particular we give two explicit descriptions of the image of the Hurewicz homomorphism for MO. One of these makes explicit the recursive computation of E. Brown and F. Peterson [1].

In Section 4 we give a variation of the theory of Section 2 which computes primitive generators of certain Hopf algebras. This theory is applied to study the primitive elements of H*(BU) and H*(SO; Z2).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 2 , 01 April 1982 , pp. 454 - 465
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Brown, E. H. and Peterson, F. P., Computation of the unoriented cobordism ring, Proc. Amer. Math. Soc. 55 (1976), 191–192.Google Scholar
2. Séminaire Henri Cartan 12ième année : 1959/60, Périodicité des groupes d'homotopie stables des groupes classiques, d'après Bott, Deux fasc, 2ième éd. (Ecole Normale Supérieure Secrétariat mathématique, Paris, 1961).Google Scholar
3. Kochman, S. O., Comodule and Hopf algebra structures for H*MU, 111. J. Math. (to appear).Google Scholar
4. Kochman, S. O., Polynomial generators for H*(BSU) and H*(BSO; Z2), Proc. Amer. Math. Soc. 84 (1982), 149–154.Google Scholar
5. Liulevicius, A., A proof of Thorn's theorem, Comment. Math. Helv. 37 (1962), 121–131.Google Scholar
6. Liulevicius, A., Notes on homotopy of Thorn spectra, Amer. J. Math. 86 (1964), 1–16.Google Scholar
7. Liulevicius, A., Immersions up to cobordism, Ill. J. Math. 19 (1975), 149–164.Google Scholar
8. Milnor, J. W., The Steenrod algebra and its dual, Ann. of Math. 67 (1958), 150–171.Google Scholar
9. Milnor, J. W. and Stasheff, J. D., Characteristic classes Ann. of Math. Studies 76 (Princeton Univ. Press, Princeton, N.J., 1974).Google Scholar