Geodesic
Degenerations of Leibniz and Anticommutative Algebras
Canadian mathematical bulletin, Tome 62 (2019) no. 3, pp. 539-549

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DOI

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.
DOI : 10.4153/S0008439519000018
Mots-clés : degeneration, rigid algebra, orbit closure, anticommutative algebra, Leibniz algebra, Lie algebra 
Ismailov, Nurlan; Kaygorodov, Ivan; Volkov, Yury. Degenerations of Leibniz and Anticommutative Algebras. Canadian mathematical bulletin, Tome 62 (2019) no. 3, pp. 539-549. doi: 10.4153/S0008439519000018
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     author = {Ismailov, Nurlan and Kaygorodov, Ivan and Volkov, Yury},
     title = {Degenerations of {Leibniz} and {Anticommutative} {Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {539--549},
     year = {2019},
     volume = {62},
     number = {3},
     doi = {10.4153/S0008439519000018},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000018/}
}
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