Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T05:45:37.714Z Has data issue: false hasContentIssue false
  • English
  • Français

H-Simple H-Module Algebras

Published online by Cambridge University Press:  20 November 2018

Miriam Cohen
Miriam Cohen*
Affiliation:
Department of Mathematics Ben Gurion University Beer Sheva, Israel
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.

Let A be an H-simple commutative H-module algebra, with AH = k and dimk H ≤ dimk A < ∞. We show that this implies that A # H is isomorphic to Mn(k), a central simple algebra. We apply this to characterize certain group graded algebras, algebras acted upon by a group as automorphisms, or by a nilpotent Lie algebra as derivations.

Keywords

16A24
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 3 , 01 September 1987 , pp. 363 - 366
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Artin, E., Nesbitt, C. and Thrall, R., Rings with minimum condition, The University of Michigan Press, Ann Arbor, 1944.Google Scholar
2. Bergen, J., Constants of Lie algebra actions, to appear.Google Scholar
3. Bergman, G. and Isaacs, I.M., Rings with fixed-point free group actions, Proc. L.M.S. 27 (1973), pp. 69–87.Google Scholar
4. Cohen, M. and Montgomery, S., Group graded rings, smash products, and group actions, Trans. AMS 586(1984), pp. 237–258.Google Scholar
5. Cohen, M. and Rowen, L.H., Group graded rings, Comm. in Algebra 11 (1983), pp. 1263–1270.Google Scholar
6. Sweedler, M., Hopf algebras, Benjamin, New York, 1969.Google Scholar