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Degenerations of Leibniz and Anticommutative Algebras

Part of: Algebraic groups General nonassociative rings Families, fibrations

Published online by Cambridge University Press:  29 January 2019

Nurlan Ismailov ,
Ivan Kaygorodov  and
Yury Volkov
Nurlan Ismailov
Affiliation:
Universidade de São Paulo, IME, São Paulo, Brazil Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan Email: nurlan.ismail@gmail.com
Ivan Kaygorodov
Affiliation:
Universidade Federal do ABCCMCC, 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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We describe all degenerations of three-dimensional anticommutative algebras $\mathfrak{A}\mathfrak{c}\mathfrak{o}\mathfrak{m}_{3}$ and of three-dimensional Leibniz algebras $\mathfrak{L}\mathfrak{e}\mathfrak{i}\mathfrak{b}_{3}$ over $\mathbb{C}$. In particular, we describe all irreducible components and rigid algebras in the corresponding varieties.

Keywords

degenerationrigid algebraorbit closureanticommutative algebraLeibniz algebraLie algebra

MSC classification

Primary: 17A32: Leibniz algebras
Secondary: 14D06: Fibrations, degenerations 14L30: Group actions on varieties or schemes (quotients)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 3 , September 2019 , pp. 539 - 549
Copyright
© Canadian Mathematical Society 2019 

Footnotes

The work was supported by FAPESP 17/15437-6, 17/21429-6; AP05131123 “Cohomological and structural problems of non-associative algebras”; RFBR 18-31-00001; the President’s Program “Support of Young Russian Scientists” (grant MK-2262.2019.1).

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