Local and 2-local automorphisms of finite-dimensional associative algebras with nil-radicals

  • F. N.Arzikulov
  • Iqboljon Karimjanov
  • Sardorbek Umrzaqov
Keywords: filiform associative algebra, null-filiform associative algebra, automorphism, local automorphism, 2-local automorphism


In the present paper automorphisms, local and 2-local automorphisms of $n$-dimensional filiform and null-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 matrix's common form on these algebras.
Therefore, these associative algebras have local automorphisms that are not automorphisms.
Also, that each 2-local automorphism of these algebras is an automorphism is proved.