Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-19T11:50:17.893Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Cohomology of Some Hopf Algebras

Published online by Cambridge University Press:  22 January 2016

Nobuo Shimada  and
Akira Iwai
Nobuo Shimada
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University
Akira Iwai
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we study certain injective resolutions for some Hopf algebras. An injective resolution for a coalgebra A with augmentation η is defined to be such an exact sequence that

where K is the basic field, Xn are injective A-comodules and δn are morphism of A-comodules.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 30 , August 1967 , pp. 103 - 111
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Adams, J.F., Stable homotopy theory (Mimeo. note), University of California, Berkeley, 1961.Google Scholar
[2] Adams, J.F., On the non-existence of elements of Hopf invariant one, Ann. of Math. 72 (1960), 20–104.Google Scholar
[3] Brown, E.H., Twisted tensor product I, Ann. of Math. 69 (1959) 223–246.Google Scholar
[4] Cartan, H., Homologie et cohomologie dúune algèbre graduée, Sémi. H. Cartan, E.N.S., 11, 1958/59, Exposé 15.Google Scholar
[5] Cartan, H., Determination des algebres H*(π,n;Zp) et H*(π, n;Zp), Sémi. H. Cartan,E.N.S., 1954/55, Exposé 9, 10.Google Scholar
[6] Lieulevicius, A.L., The cohomology of a subalgebra of the Steenrod algebra, Trans. A.M.S. 104 (1962), 443–449.Google Scholar
[7] Massey, W.S., Some higher order cohomology operations, Symposium internacinal de topologia algebrica, Universidad Nacional Autónoma de México and UNESCO, Mexico City, 1958, 145–154.Google Scholar
[8] May, J.P., The cohomology of restricted Lie algebras and of Hopf algebras (Mimeo. note), Princeton University, 1964.Google Scholar
[9] Milnor, J., The Steenrod algebra and its dual, Ann. of Math. 67 (1958), 150–171.Google Scholar
[10] Milnor, J. and Moore, J.C., On the structure of Hopf algebras, Ann. of Math. 81 (1965), 211–264.Google Scholar
[11] Shimada, N. and Iwai, A., A remark on resolutions for Hopf algebras, Publication of the Research Institute for Mathematical Sciences, Kyoto University, Ser, A, Vol. 1, No. 2 1966).Google Scholar
[12] Steenrod, N.E., Cohomology operations, Ann. of Math. Studies 50, Princeton, 1962.Google Scholar