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Register a new userAnticommutative Engel algebras of the first five levels
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Authors
Yury Volkov
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Anticommutative Engel algebras of the first five degeneration levels are classified. All algebras appearing in this classification are nilpotent Malcev algebras.
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We describe all degenerations of three dimensional anticommutative algebras $mathfrak{Acom}_3$ and of three dimensional Leibniz algebras $mathfrak{Leib}_3$ over $mathbb{C}.$ In particular, we describe all irreducible components and rigid algebras in the corresponding varieties
We study anticommutative algebras with the property that commutator of any two multiplications is a derivation.
$n$-ary algebras of the first degeneration level are described. A detailed classification is given in the cases $n=2,3$.
We investigate a method of construction of central deformations of associative algebras, which we call centrification. We prove some general results in the case of Hopf algebras and provide several examples.
In this paper, we introduce the notion of bigraft algebra, generalizing the notions of left and right graft algebras. We give a combinatorial description of the free bigraft algebra generated by one generator and we endow this algebra with a Hopf algebra structure, and a pairing. Next, we study the Koszul dual of the bigraft operad and we give a combinatorial description of the free dual bigraft algebra generated by one generator. With the help of a rewriting method, we prove that the bigraft operad is Koszul. Finally, we define the notion of infinitesimal bigraft bialgebra and we prove a rigidity theorem for connected infinitesimal bigraft bialgebras.
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