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Degenerations of Leibniz and Anticommutative Algebras

  • Nurlan Ismailov (a1) (a2), Ivan Kaygorodov (a3) and Yury Volkov (a4)

Abstract

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.

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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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Degenerations of Leibniz and Anticommutative Algebras

  • Nurlan Ismailov (a1) (a2), Ivan Kaygorodov (a3) and Yury Volkov (a4)

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