The coordinate ring of an $n$-dimensional sphere and some examples of differentially simple algebras

V. N. Zhelyabin; A. A. Popov; I. P. Shestakov

Geodesic

Parcourir par

The coordinate ring of an $n$-dimensional sphere and some examples of differentially simple algebras

V. N. Zhelyabin ; A. A. Popov ; I. P. Shestakov

Algebra i logika, Tome 52 (2013) no. 4, pp. 416-434

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

Résumé

Using the coordinate ring of an $n$-dimensional real sphere, we construct examples of differentially simple algebras which are finitely generated projective, but nonfree, modules over their centroids. As a consequence, examples of such algebras are obtained in varieties of associative, Lie, alternative, Mal'tsev, and Jordan algebras.

Keywords: differentially simple algebra, variety, Lie algebra, alternative algebra, Mal’tsev algebra, Jordan algebra.
Mots-clés : module, centroid

@article{AL_2013_52_4_a1,
     author = {V. N. Zhelyabin and A. A. Popov and I. P. Shestakov},
     title = {The coordinate ring of an $n$-dimensional sphere and some examples of differentially simple algebras},
     journal = {Algebra i logika},
     pages = {416--434},
     publisher = {mathdoc},
     volume = {52},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2013_52_4_a1/}
}

TY  - JOUR
AU  - V. N. Zhelyabin
AU  - A. A. Popov
AU  - I. P. Shestakov
TI  - The coordinate ring of an $n$-dimensional sphere and some examples of differentially simple algebras
JO  - Algebra i logika
PY  - 2013
SP  - 416
EP  - 434
VL  - 52
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2013_52_4_a1/
LA  - ru
ID  - AL_2013_52_4_a1
ER  -

%0 Journal Article
%A V. N. Zhelyabin
%A A. A. Popov
%A I. P. Shestakov
%T The coordinate ring of an $n$-dimensional sphere and some examples of differentially simple algebras
%J Algebra i logika
%D 2013
%P 416-434
%V 52
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2013_52_4_a1/
%G ru
%F AL_2013_52_4_a1

V. N. Zhelyabin; A. A. Popov; I. P. Shestakov. The coordinate ring of an $n$-dimensional sphere and some examples of differentially simple algebras. Algebra i logika, Tome 52 (2013) no. 4, pp. 416-434. http://geodesic.mathdoc.fr/item/AL_2013_52_4_a1/