In this paper we generalize the Skjelbred–Sund method, used to classify nilpotent Lie algebras, in order to classify triple systems with non-zero annihilator. We develop this method with the purpose ...of classifying nilpotent Lie triple systems, obtaining from it the algebraic classification of the nilpotent Lie triple systems up to dimension four. Additionally, we obtain the geometric classification of the variety of nilpotent Lie triple systems up to dimension four.
In this work, we study a linear operator f on a pre-Euclidean space V by using properties of a corresponding graph. Given a basis B of V, we present a decomposition of V as an orthogonal direct sum ...of certain linear subspaces {Ui}i∈I, each one admitting a basis inherited from B, in such way that f=∑i∈Ifi. Each fi is a linear operator satisfying certain conditions with respect to Ui. Considering this new hypothesis, we assure the existence of an isomorphism between the graphs of f relative to two different bases. We also study the minimality of V by using the graph of f relative to B.
The paper is devoted to classify nilpotent Jordan algebras of dimension up to five over an algebraically closed field F of characteristic not 2. We obtained a list of 35 isolated non-isomorphic ...5-dimensional nilpotent non-associative Jordan algebras and 6 families of non-isomorphic 5-dimensional nilpotent non-associative Jordan algebras depending either on one or two parameters over an algebraically closed field of characteristic ≠2,3. In addition to these algebras we obtained two non-isomorphic 5-dimensional nilpotent non-associative Jordan algebras over an algebraically closed field of characteristic 3.
The paper is devoted to the study of annihilator extensions of evolution algebras and suggests an approach to classify finite-dimensional nilpotent evolution algebras. Subsequently nilpotent ...evolution algebras of dimension up to four are classified.
The paper is devoted to the study of annihilator extensions of Jordan algebras and suggests new approach to classify nilpotent Jordan algebras, which is analogous to the Skjelbred-Sund method for ...classifying nilpotent Lie algebras
2
,
4
,
15
. Subsequently, we have classified nilpotent Jordan algebras of dimension up to four.
In this paper we give a complete classification of all n-dimensional non-Lie Malcev algebras with (n−4)-dimensional annihilator over an algebraically closed field of characteristic 0. We also show ...that such algebras are special.
The paper is devoted to give a complete classification of all n-dimensional non-associative Jordan algebras with (n−3)-dimensional annihilator over an algebraically closed field of characteristic ≠2. ...We also give a complete classification of all n-dimensional Jordan algebras with (n−1)- and (n−2)-dimensional annihilator.
We generalize the Skjelbred–Sund method, used to classify nilpotent low-dimensional Lie algebras, in order to classify Poisson algebras with non-trivial annihilator. We develop this method with the ...purpose of classifying nilpotent Poisson algebras, obtaining from it the algebraic classification of the nilpotent Poisson algebras up to dimension four. Additionally, we obtain the geometric classification of the variety of nilpotent Poisson algebras up to dimension four, by adapting some notions and results used for varieties of algebras with a single multiplication.
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