Local and $2$-local automorphisms of null-filiform and filiform associative algebras

Source abstract

In the present paper automorphisms, local and $2$-local automorphisms of $n$-dimensional null-filiform and filiform associative algebras are studied. Namely, a common form of the matrix of automorphisms and local automorphisms of these algebras is clarified. It turns out that the common form of the matrix of an automorphism on these algebras does not coincide with the local automorphism's matrices common form on these algebras. Therefore, these associative algebras have local automorphisms that are not automorphisms. Also, that each $2$-local automorphism of null-filiform algebra is an automorphism and some associative filiform algebras admit $2$-local automorphisms which are not automorphisms are proved. Received: 11 February 2023 | Accepted: 2 April 2024