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The structure of split regular Hom-Poisson algebras

María J. Aragón Periñán, Antonio J. Calderón Martín (2016)

Colloquium Mathematicae

We introduce the class of split regular Hom-Poisson algebras formed by those Hom-Poisson algebras whose underlying Hom-Lie algebras are split and regular. This class is the natural extension of the ones of split Hom-Lie algebras and of split Poisson algebras. We show that the structure theorems for split Poisson algebras can be extended to the more general setting of split regular Hom-Poisson algebras. That is, we prove that an arbitrary split regular Hom-Poisson algebra is of the form = U + ∑ j I j with U...

The variety of dual mock-Lie algebras

Luisa M. Camacho, Ivan Kaygorodov, Viktor Lopatkin, Mohamed A. Salim (2020)

Communications in Mathematics

We classify all complex 7 - and 8 -dimensional dual mock-Lie algebras by the algebraic and geometric way. Also, we find all non-trivial complex 9 -dimensional dual mock-Lie algebras.

The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

Abanina, L., Mishchenko, S. (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30Let F be a field of characteristic zero. In this paper we study the variety of Leibniz algebras 3N determined by the identity x(y(zt)) ≡ 0. The algebras of this variety are left nilpotent of class not more than 3. We give a complete description of the vector space of multilinear identities in the language of representation theory of the symmetric group Sn and Young diagrams. We also show that the...

The Wells map for abelian extensions of 3-Lie algebras

Youjun Tan, Senrong Xu (2019)

Czechoslovak Mathematical Journal

The Wells map relates automorphisms with cohomology in the setting of extensions of groups and Lie algebras. We construct the Wells map for some abelian extensions 0 → A ↪ L → π B → 0 of 3-Lie algebras to obtain obstruction classes in H 1 ( B , A ) for a pair of automorphisms in Aut ( A ) × Aut ( B ) to be inducible from an automorphism of L . Application to free nilpotent 3-Lie algebras is discussed.

Toward ternary C

Geoffrey Dixon (2010)

Commentationes Mathematicae Universitatis Carolinae

In which the binary product algebra of complex numbers, C, is generalized to a ternary product algebra, 𝐂 3 .

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