TY - JOUR

T1 - Degenerations of nilpotent algebras

AU - Fernández Ouaridi, Amir

AU - Kaygorodov, Ivan

AU - Khrypchenko, Mykola

AU - Volkov, Yury

N1 - Publisher Copyright: © 2021 Elsevier B.V.

PY - 2022/3

Y1 - 2022/3

N2 - We give a complete description of the primary degenerations and non-degenerations between the 3-dimensional nilpotent algebras, the 4-dimensional nilpotent commutative algebras and the 5-dimensional nilpotent anticommutative algebras over C. It follows that all the varieties under consideration are irreducible and determined by the rigid algebra N2, the family of algebras C19(α) and the rigid algebra A11, respectively. In particular, as an auxiliary new result, we obtain an algebraic classification of the 4-dimensional complex nilpotent commutative algebras.

AB - We give a complete description of the primary degenerations and non-degenerations between the 3-dimensional nilpotent algebras, the 4-dimensional nilpotent commutative algebras and the 5-dimensional nilpotent anticommutative algebras over C. It follows that all the varieties under consideration are irreducible and determined by the rigid algebra N2, the family of algebras C19(α) and the rigid algebra A11, respectively. In particular, as an auxiliary new result, we obtain an algebraic classification of the 4-dimensional complex nilpotent commutative algebras.

KW - Algebraic classification

KW - Anticommutative algebra

KW - Commutative algebra

KW - Geometric classification

KW - Nilpotent algebra

UR - http://www.scopus.com/inward/record.url?scp=85111329797&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/926dbcbf-b10c-320c-bb98-4687c54bb607/

U2 - 10.1016/j.jpaa.2021.106850

DO - 10.1016/j.jpaa.2021.106850

M3 - Article

AN - SCOPUS:85111329797

VL - 226

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 3

M1 - 106850

ER -