Geodesic
Composition algebras of the second kind
Algebra i logika, Tome 46 (2007) no. 4, pp. 428-447.

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

The concept of a composition algebra of the second kind is introduced. We prove that such algebras are non-degenerate monocomposition algebras without unity. A big number of these algebras in any finite dimension are constructed, as well as two algebras in a countable dimension. The constructed algebras each contains a non-isotropic idempotent $e^2=e$. We describe all orthogonally non-isomorphic composition algebras of the second kind in the following forms: (1) a two-dimensional algebra (which has turned out to be unique); (2) three-dimensional algebras in the constructed series. For every algebra $A$, the group $\operatorname{Ortaut}A$ of orthogonal automorphisms is specified.
Keywords: composition algebra of the second kind, group of orthogonal automorphisms of algebras, non-degenerate monocomposition algebra, commutative algebra, anticommutative algebra.
Mots-clés : orthogonal isomorphism of algebras 
@article{AL_2007_46_4_a1,
     author = {A. T. Gainov},
     title = {Composition algebras of the second kind},
     journal = {Algebra i logika},
     pages = {428--447},
     publisher = {mathdoc},
     volume = {46},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2007_46_4_a1/}
}
TY  - JOUR
AU  - A. T. Gainov
TI  - Composition algebras of the second kind
JO  - Algebra i logika
PY  - 2007
SP  - 428
EP  - 447
VL  - 46
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2007_46_4_a1/
LA  - ru
ID  - AL_2007_46_4_a1
ER  - 
%0 Journal Article
%A A. T. Gainov
%T Composition algebras of the second kind
%J Algebra i logika
%D 2007
%P 428-447
%V 46
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2007_46_4_a1/
%G ru
%F AL_2007_46_4_a1
A. T. Gainov. Composition algebras of the second kind. Algebra i logika, Tome 46 (2007) no. 4, pp. 428-447. http://geodesic.mathdoc.fr/item/AL_2007_46_4_a1/

[1] K. A. Zhevlakov, A. M. Slinko, I. P. Shestakov, A. I. Shirshov, Koltsa, blizkie k assotsiativnym, Nauka, M., 1978 | MR | Zbl

[2] A. T. Gainov, “Monokompozitsionnye algebry”, Sib. matem. zh., 10:1 (1969), 3–30 | MR

[3] H. P. Petersson, “The classification of two-dimensional nonassociative algebras”, Result. Math., 37:1–2 (2000), 120–154 | MR | Zbl