Geodesic
The order of algebras with nontrivial fixed point subalgebras
Lobachevskii journal of mathematics, Tome 25 (2007), pp. 187-196.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper represents an advancement of research the fundamental problem of which is a classification of algebras A (Weil algebras primarily) having a nontrivial fixed point subalgebra (with respect to \underline{all} algebra automorphisms). The main result is the determination of the algebra order allowing a nontrivial fixed point subalgebra. Moreover, an autonomous importance of some results about socle elements of A and the unipotency of algebra automorphisms is highlighted.
Keywords: Local algebra
Mots-clés : automorphism. 
@article{LJM_2007_25_a4,
     author = {M. Kure\v{s} and D. Sehnal},
     title = {The order of algebras with nontrivial fixed point subalgebras},
     journal = {Lobachevskii journal of mathematics},
     pages = {187--196},
     publisher = {mathdoc},
     volume = {25},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2007_25_a4/}
}
TY  - JOUR
AU  - M. Kureš
AU  - D. Sehnal
TI  - The order of algebras with nontrivial fixed point subalgebras
JO  - Lobachevskii journal of mathematics
PY  - 2007
SP  - 187
EP  - 196
VL  - 25
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2007_25_a4/
LA  - en
ID  - LJM_2007_25_a4
ER  - 
%0 Journal Article
%A M. Kureš
%A D. Sehnal
%T The order of algebras with nontrivial fixed point subalgebras
%J Lobachevskii journal of mathematics
%D 2007
%P 187-196
%V 25
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2007_25_a4/
%G en
%F LJM_2007_25_a4
M. Kureš; D. Sehnal. The order of algebras with nontrivial fixed point subalgebras. Lobachevskii journal of mathematics, Tome 25 (2007), pp. 187-196. http://geodesic.mathdoc.fr/item/LJM_2007_25_a4/

[1] Guil-Asensio, F., Saorín, M., “The group of automorphisms of a commutative algebra”, Mathematische Zeitschrift, 219 (1995), 31–48 | DOI | MR | Zbl

[2] Kharchenko, V. K., Automorphisms and Derivations of Associative Rings, Kluwer Academic Publishers, Dordrecht / Boston / London, 1991 | MR | Zbl

[3] Kolář, I., Michor, P. W. and Slovák, J., Natural Operations in Differential Geometry, Springer-Verlag, 1993 | MR

[4] Kureš, M., “Weil modules and gauge bundles”, Acta Mathematica Sinica (English Series), 22:1 (2006), 271–278 | DOI | MR | Zbl

[5] Kureš, M., Mikulski, W. M., “Natural operators lifting vector fields to bundles of Weil contact elements”, Czechoslovak Mathematical Journal, 54:129 (2004), 855–867 | DOI | MR | Zbl

[6] Kureš, M., Mikulski, W. M., “Natural operators lifting 1-forms to bundles of Weil contact elements”, Bulletin of the Irish Mathematical Society, 49 (2002), 23–41 | MR | Zbl

[7] Pollack, R. D., “Algebras and their automorphism groups”, Communications in Algebra, 17:8 (1989), 1843–1866 | DOI | MR | Zbl

[8] Weil, A., “Théorie des points proches sur les variétés différentiables (French)”, Géométrie différentielle, Colloques Internationaux du Centre National de la Recherche Scientifique, (Strasbourg, 1953), 111–117 | MR | Zbl