Geodesic
Variety of Jordan algebras in small dimensions
Algebra and discrete mathematics, no. 2 (2006), pp. 62-76.

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The variety $\mathcal{J}or_n$ of Jordan unitary algebra structures on $\bf{k}^n$, $\bf{k}$ an algebraically closed field with char $\bf {k}\neq 2$, is studied, as well as infinitesimal deformations of Jordan algebras. Also we establish the list of $\rm{GL}_n$-orbits on $\mathcal{J}or_n$, $n=4,5$ under the action of structural transport. The numbers $jor_4$ and $jor_5$ of irreducible components are 3 and 6 respectively; a list of generic structures is included. 
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     author = {Iryna Kashuba},
     title = {Variety of {Jordan} algebras in small dimensions},
     journal = {Algebra and discrete mathematics},
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     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2006_2_a7/}
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Iryna Kashuba. Variety of Jordan algebras in small dimensions. Algebra and discrete mathematics, no. 2 (2006), pp. 62-76. http://geodesic.mathdoc.fr/item/ADM_2006_2_a7/