Classification of ($\rho,\tau,\sigma$)-derivations of two-dimensional left-symmetric dialgebras

TL;DR

This paper introduces a generalized concept of derivations for dendriform algebras and provides a complete classification of these derivations for two-dimensional left-symmetric dialgebras over a field.

Contribution

It defines all admissible parameter values for generalized derivations and classifies them for two-dimensional left-symmetric dialgebras.

Findings

Complete classification of ($ ho, au,\sigma$)-derivations for 2D left-symmetric dialgebras

Identification of all admissible parameter values for these derivations

Extension of derivation theory to dendriform algebra structures

Abstract

We introduce and study a generalized form of derivations for dendriform algebras, specifying all admissible parameter values that define these derivations. Additionally, we present a complete classification of generalized derivations for two-dimensional left-symmetric dialgebras over the field $\mathbb{K}$.