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Algebra Logika, 2007, Volume 46, Number 4, Pages 428–447 (Mi al306)  

Composition algebras of the second kind

A. T. Gainov


Abstract: 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, orthogonal isomorphism of algebras, group of orthogonal automorphisms of algebras, non-degenerate monocomposition algebra, commutative algebra, anticommutative algebra.

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English version:
Algebra and Logic, 2007, 46:4, 231–243

Bibliographic databases:

UDC: 512.554
Received: 11.10.2006
Revised: 23.04.2007

Citation: A. T. Gainov, “Composition algebras of the second kind”, Algebra Logika, 46:4 (2007), 428–447; Algebra and Logic, 46:4 (2007), 231–243

Citation in format AMSBIB
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\paper Composition algebras of the second kind
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\issue 4
\pages 428--447
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\pages 231--243
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