Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-12T22:32:50.646Z Has data issue: false hasContentIssue false
  • English
  • Français

A Remark on the Loewy-Series of Certain Hopf Algebras

Published online by Cambridge University Press:  20 November 2018

Frank Röhl
Frank Röhl*
Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487 USA
Rights & Permissions [Opens in a new window]

Abstract

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.

An easy proof will be given to show that for finite dimensional Hopf-algebras with nilpotent augmentation ideal over the field of p elements, the upper and lower Loewy-series coincide. In particular, this holds for the restricted universal envelope of nilpotent Lie-p-algebras with nilpotent p-map.

Keywords

16A2417B50
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 2 , 01 June 1989 , pp. 190 - 193
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras, Interscience 1962.Google Scholar
2. Hill, E. T., “The annihilator of radical powers in the modular group ring of a p-group“, Proc. Amer. Math. Soc. 25 (1970), 811-815.Google Scholar
3. Huppert, B. and Blackburn, N., Finite groups II, Springer 1982.Google Scholar
4. Jacobson, N., Restricted Lie algebras of characteristic p, Transactions Amer. Math. Soc. 50 (1941), 15-25.Google Scholar
5. Larson, R. G. and weedier, M. E. S, An associative orthogonal bilinear form for Hopf algebras, Amer. J. Math. 91 (1969), 75-94.Google Scholar
6. Quillen, D. G., Rational homotopy theory, Ann. Math. 90 (1969), 205-295.Google Scholar
7. Sweedler, M. E., “Hopf algebras'', Benjamin 1969.Google Scholar