The classification of N-dimensional non-associative Jordan algebras with (N − 3)-dimensional annihilator

The Algebraic and Geometric Classification of Nilpotent Bicommutative Algebras

“…With this background, it comes as no surprise that the central extensions of Lie and non-Lie algebras have been exhaustively studied for years. It is interesting both to describe them and to use them to classify different varieties of algebras [2,28,29,34,39,40]. Firstly, Skjelbred and Sund devised a method for classifying nilpotent Lie algebras employing central extensions [39].…”

The algebraic and geometric classification of nilpotent anticommutative algebras

“…Skjelbred and Sund [49] used central extensions of Lie algebras to classify nilpotent Lie algebras. In later works, using the same method, all non-Lie central extensions of 4-dimensional Malcev algebras [31], all non-associative central extensions of 3-dimensional Jordan algebras [30], all anticommutative central extensions of 3-dimensional anticommutative algebras [10] and all central extensions of 2-dimensional algebras [12] were described, to mention but a few. Related work on central extensions can be found, for example, in [2,37,50].…”

The algebraic classification of nilpotent Tortkara algebras

“…The algebraic study of central extensions of Lie and non-Lie algebras has a very long history [2,20,21,25,33,35]. Thus, Skjelbred and Sund used central extensions of Lie algebras for a classification of nilpotent Lie algebras [33].…”

“…Thus, Skjelbred and Sund used central extensions of Lie algebras for a classification of nilpotent Lie algebras [33]. After that, the method introduced by Skjelbred and Sund was used to describe all non-Lie central extensions of all 4-dimensional Malcev algebras [21], all non-associative central extensions of 3-dimensional Jordan algebras [20], all anticommutative central extensions of 3-dimensional anticommutative algebras [6], all central extensions of 2-dimensional algebras [7]. The method of central extensions was used to describe all 4-dimensional nilpotent associative algebras [12], all 4-dimensional nilpotent bicommutative algebras [26], all 4-dimensional nilpotent Novikov algebras [24], all 5-dimensional nilpotent Jordan algebras [19], all 5-dimensional nilpotent restricted Lie algebras [11], all 6-dimensional nilpotent Lie algebras [10,13], all 6-dimensional nilpotent Malcev algebras [22], all 6-dimensional nilpotent binary Lie algebras [3], all 6-dimensional nilpotent anticommutative CD-algebras [3] and some other.…”