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

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 e1,e2,...,em,... 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.

Keywords

• Zinbiel (dual Leibniz) algebra
• universal (multiplicative) enveloping algebra
• basis
• automorphism
• affine automorphism