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

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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/}
}
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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/