Variety of Jordan algebras in small dimensions
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...
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| Date: | 2018 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/889 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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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