An Algorithmic Approach to Inner Derivations of Low-Dimensional Zinbiel Algebras

TL;DR

This paper develops an algorithm to characterize inner derivations of low-dimensional Zinbiel algebras and applies it to explicitly describe their properties in dimensions two to four.

Contribution

It introduces a novel algorithmic method for analyzing inner derivations in low-dimensional Zinbiel algebras, with explicit applications to small dimensions.

Findings

Explicit descriptions of inner derivations for 2, 3, and 4-dimensional Zinbiel algebras

Development of a matrix-based algorithm for inner derivations

Enhanced understanding of algebraic structure of Zinbiel algebras

Abstract

In this paper, we introduce the concept of inner derivations of low-dimensional Zinbiel algebras and investigate their properties. The primary objective of this study is to develop an algorithm to characterize the inner derivations of any n-dimensional Zinbiel algebra in matrix form. Additionally, we apply this algorithm to two, three and four-dimensional complex Zinbiel algebras, providing explicit descriptions of their inner derivations.