Geodesic
H-Simple H-Module Algebras
Canadian mathematical bulletin, Tome 30 (1987) no. 3, pp. 363-366

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1987-052-0
Mots-clés : 16A24 
Cohen, Miriam. H-Simple H-Module Algebras. Canadian mathematical bulletin, Tome 30 (1987) no. 3, pp. 363-366. doi: 10.4153/CMB-1987-052-0
@article{10_4153_CMB_1987_052_0,
     author = {Cohen, Miriam},
     title = {H-Simple {H-Module} {Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {363--366},
     year = {1987},
     volume = {30},
     number = {3},
     doi = {10.4153/CMB-1987-052-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-052-0/}
}
TY  - JOUR
AU  - Cohen, Miriam
TI  - H-Simple H-Module Algebras
JO  - Canadian mathematical bulletin
PY  - 1987
SP  - 363
EP  - 366
VL  - 30
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-052-0/
DO  - 10.4153/CMB-1987-052-0
ID  - 10_4153_CMB_1987_052_0
ER  - 
%0 Journal Article
%A Cohen, Miriam
%T H-Simple H-Module Algebras
%J Canadian mathematical bulletin
%D 1987
%P 363-366
%V 30
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-052-0/
%R 10.4153/CMB-1987-052-0
%F 10_4153_CMB_1987_052_0

[1] 1. Artin, E., Nesbitt, C. and Thrall, R., Rings with minimum condition, The University of Michigan Press, Ann Arbor, 1944. Google Scholar

[2] 2. Bergen, J., Constants of Lie algebra actions, to appear. Google Scholar

[3] 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] 4. Cohen, M. and Montgomery, S., Group graded rings, smash products, and group actions, Trans. AMS 586(1984), pp. 237–258. Google Scholar

[5] 5. Cohen, M. and Rowen, L.H., Group graded rings, Comm. in Algebra 11 (1983), pp. 1263–1270. Google Scholar

[6] 6. Sweedler, M., Hopf algebras, Benjamin, New York, 1969. Google Scholar

Cité par Sources :