Degenerations of Jordan Superalgebras

The geometric classification of nilpotent Tortkara algebras

“…There is only one 6-dimensional nilpotent non-metabelian Tortkara algebra: T 6 19 . Obviously, T 6 19 is rigid.…”

The Algebraic and Geometric Classification of Nilpotent Bicommutative Algebras

“…It is typical to focus on small dimensions, and there are two main directions for the classification: algebraic and geometric. Varieties as Jordan, Lie, Leibniz or Zinbiel algebras have been studied from these two approaches ( [1, 9, 12-15, 22, 27, 30, 37] and [3,5,6,9,11,22,24,25,31,32,[35][36][37][38], respectively). In the present paper, we give the algebraic and geometric classification of 4-dimensional nilpotent bicommutative algebras.…”

The algebraic and geometric classification of nilpotent anticommutative algebras

“…(i) α 3 α 5 − α 1 α 6 = 0. Then we will choose x, z such that 6 and v = α 5 , so that α * 6 = 0. Considering α * 2 = α * 4 = 0 as a linear system in h and w, we see that it has a unique solution…”