Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T13:08:31.141Z Has data issue: false hasContentIssue false
  • English
  • Français

On Extending Projectives of Finite Group-Graded Algebras

Published online by Cambridge University Press:  20 November 2018

Morton E. Harris
Morton E. Harris*
Affiliation:
School of Mathematics University of Minnesota Minneapolis, Minnesota 55455
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 G be a finite group, let k be a field and let R be a finite dimensional fully G-graded k-algebra. Also let L be a completely reducible R-module and let P be a projective cover of R. We give necessary and sufficient conditions for P|R1 to be a projective cover of L|R1 in Mod (R1). In particular, this happens if and only if L is R1-projective. Some consequences in finite group representation theory are deduced.

Keywords

16A0316A26.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 2 , 01 June 1991 , pp. 224 - 228
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Cartan, H. and Eilenberg, S., Homological Algebra, Princeton University, Princeton, 1956.Google Scholar
2. Cohen, M. and Montgomery, S., Group-Graded Rings, Smash Products, and Group Actions, Trans. A.M.S. 282 (1984), 237–258.Google Scholar
3. Curtis, C. W. and Reiner, I., Methods of Representation Theory, vol. I, John Wiley and Sons, New York, 1981.Google Scholar
4. Dade, E. C., Isomorphisms of Clifford Extensions, Ann. of Math. 92 (1970), 375–433.Google Scholar
5. Dade, E. C., Group-Graded Rings and Modules, Math Z. 174 (1980), 241–262.Google Scholar
6. Dade, E. C., The equivalence of various generalizations of group rings and modules, Math. Z. 181 (1982), 335–344.Google Scholar
7. Feit, W., The Representation Theory of Finite Groups, North-Holland, Amsterdam, 1982.Google Scholar
8. Harris, M. E., Filtrations, Stable Clifford Theory and Group-Graded Rings and Modules, Math. Z. 196 (1987), 497–510.Google Scholar
9. Harris, M. E., Clifford theory and filtrations, J. of Algebra. 132 (1990), 205–218.Google Scholar
10. Huppert, B., Endliche Gruppen I, Springer-Verlag, Berlin, 1967.Google Scholar
11. Huppert, B. and Blackburn, N., Finite Groups II, Springer-Verlag, Berlin, 1982.Google Scholar
12. Willems, W., On the projective s of a group algebra Math. Z. 171 (1980), 163–174.Google Scholar