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The Variety of Two-dimensional Algebras Over an Algebraically Closed Field

Part of: Algebraic groups

Published online by Cambridge University Press:  16 October 2018

Ivan Kaygorodov  and
Yury Volkov
Ivan Kaygorodov
Affiliation:
Universidade Federal do ABC, CMCC, Santo André, Brazil Email: kaygorodov.ivan@gmail.com
Yury Volkov
Affiliation:
Saint Petersburg State University, Saint Petersburg, Russia Email: wolf86_666@list.ru
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Abstract

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The work is devoted to the variety of two-dimensional algebras over algebraically closed fields. First we classify such algebras modulo isomorphism. Then we describe the degenerations and the closures of certain algebra series in the variety of two-dimensional algebras. Finally, we apply our results to obtain analogous descriptions for the subvarieties of flexible and bicommutative algebras. In particular, we describe rigid algebras and irreducible components for these subvarieties.

Keywords

two-dimensional algebrasorbit closuredegenerationrigid algebra

MSC classification

Primary: 14L30: Group actions on varieties or schemes (quotients)
Type
Article
Information
Canadian Journal of Mathematics , Volume 71 , Issue 4 , August 2019 , pp. 819 - 842
Copyright
© Canadian Mathematical Society 2018 

Footnotes

The work was supported by FAPESP 14/24519-8; RFBR 17-51-04004; the President’s Program “Support of Young Russian Scientists” (grant MK-1378.2017.1).

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