The classification of 5-dimensional complex nilpotent associative algebras

Аннотация

In this paper we give the classification of 5-dimensional complex nilpotent associative algebras. We use χ(A)=(dimA,dimA2,dimA3,…,dimAn) - the isomorphism invariant. We prove that there are only two possible isomorphism invariants χ(A)=(5,2,1,0,0) or χ(A)=(5,3,1,0,0) for any 5-dimensional complex nilpotent associative algebra A with the condition A4=0∧A3≠0 and we give the classification (up to isomorphism) of such type algebras. 5-dimensional complex nilpotent associative algebras with the conditions A6=0∧A5≠0,A5=0∧A4≠0 and A3=0∧A2≠0 have already been classified. Thus, we complete the classification of 5-dimensional complex nilpotent associative algebras.

Темы

Идентификаторы

DOI

10.1080/00927872.2020.1822371

Цитирования и источники