Description of local multipliers on finite-dimensional associative algebras - Arzikulov, Farhodjon; Samsaqov, Odiljon (Journal of the Belarusian State University. Mathematics and Informatics, 2023)
In 2020 F. Arzikulov and N. Umrzaqov introduced the concept of a (linear) local multiplier. They proved that every local left (right) multiplier on the matrix ring over a division ring is a left (right, respectively) multiplier. This paper is devoted to (linear) local weak left (right) multipliers on 5-dimensional naturally graded 2-filiform non-split associative algebras. An algorithm for obtaining a common form of the matrices of the weak left (right) multipliers on the 5-dimensional naturally graded 2-filiform non-split associative algebras λ15 and λ25, constructed by I. Karimjanov and M. Ladra, is developed. An algorithm for obtaining a general form of the matrices of the local weak left (right) multipliers on the algebras λ15 and λ25 is also developed. It turns out that the associative algebras λ15 and λ25 have a local weak left (right) multiplier that is not a weak left (right, respectively) multiplier.