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arXiv · 1507.02324

Conservative algebras of $2$-dimensional algebras, II

Ivan Kaygorodov·Yury Volkov
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Abstract

In 1990 Kantor defined the conservative algebra $W(n)$ of all algebras (i.e. bilinear maps) on the $n$-dimensional vector space. If $n>1$, then the algebra $W(n)$ does not belong to any well-known class of algebras (such as associative, Lie, Jordan, or Leibniz algebras). We describe automorphisms, one-sided ideals, and idempotents of $W(2).$ Also similar problems are solved for the algebra $W_2$ of all commutative algebras on the 2-dimensional vector space and for the algebra $S_2$ of all commutative algebras with trace zero multiplication on the 2-dimensional vector space.

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Ivan Kaygorodov, Yury Volkov. 2015-07-08. Conservative algebras of $2$-dimensional algebras, II. https://doi.org/10.1080/00927872.2016.1236935

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