# Automorphisms of the universal enveloping algebra of a finite-dimensional Zinbiel algebra with zero multiplication

## DOI:

https://doi.org/10.31489/2023m4/173-184## Keywords:

Zinbiel (dual Leibniz) algebra, universal (multiplicative) enveloping algebra, basis, automorphism, affine automorphism## Abstract

In recent years there has been a great interest in the study of Zinbiel (dual Leibniz) algebras. Let *A *be Zinbiel algebra over an arbitrary field *K *and let *e*_{1}*,e*_{2}*,...,e _{m},... *be a linear basis of

*A*. In 2010 A. Naurazbekova, using the methods of Gro¨bner-Shirshov bases, constructed the basis of the universal (multiplicative) enveloping algebra

*U*(

*A*) of

*A*. Using this result, the automorphisms of the universal enveloping algebra of a finite-dimensional Zinbiel algebra with zero multiplication are described.