On the classification of bilinear maps with radical of a fixed codimension

Unified computational approach to nilpotent algebra classification problems

“…3.1 Choosing three dimensional Moufang algebras from the literature As mentioned before, various three dimensional nilpotent algebra classifications were considered in [4] including Moufang algebras. For our purposes, we need to extract the three dimensional algebras from this article.…”

“…Now the code has all the information that it needs. Next we select from [17] all two dimensional Moufang algebras and from [4] three dimensional nilpotent Moufang algebras by using the following code: Remark. It follows from Theorem 3.3 in [17] that any nontrivial 2-dimensional Moufang algebra is isomorphic to one of the M 2 0i algebras, where i ∈ {1, .…”

The algebraic classification of nilpotent commutative CD-algebras

“…Method of classification of nilpotent algebras. Throughout this paper, we use the notations and methods well written in [7,23,24], which we have adapted for the CCD case with some modifications. Further in this section we give some important definitions.…”

“…4-dimensional CCD-algebras. Thanks to [7] we have an algebraic classification of all complex 4dimensional nilpotent CCD-algebras with 2and 3-dimensional annihilator: Here we will collect all information about C 3 * 01 : Algebra Multiplication Cohomology Automorphisms…”

“…Skjelbred and Sund [49] used central extensions of Lie algebras to classify nilpotent Lie algebras. Using the same method, all non-Lie central extensions of all 4-dimensional Malcev algebras [24], all non-associative central extensions of all 3-dimensional Jordan algebras [23], all anticommutative central extensions of 3-dimensional anticommutative algebras [5], all central extensions of 2-dimensional algebras [7] and some others were described. One can also look at the classification of 3-dimensional nilpotent algebras [18], 4-dimensional nilpotent associative algebras [16], 4-dimensional nilpotent Novikov algebras [30], 4-dimensional nilpotent bicommutative algebras [38], 4-dimensional nilpotent commutative algebras in [18], 4-dimensional nilpotent CD-algebras in [32], 5-dimensional nilpotent restricted Lie agebras [14], 5-dimensional nilpotent Jordan algebras [22], 5-dimensional nilpotent anticommutative algebras [18], 6-dimensional nilpotent Lie algebras [11,15], 6dimensional nilpotent Malcev algebras [25], 6-dimensional nilpotent Tortkara algebras [20], 6-dimensional nilpotent binary Lie algebras [1], 6-dimensional nilpotent anticommutative CD-algebras [1], 8-dimensional dual mock-Lie algebras [10].…”