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Classification of ($ρ,τ,σ$)-derivations of two-dimensional left-symmetric dialgebras

Basdouri Imed, Bouzid Mosbahi

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 $\mathbb{K}$.

Classification of ($ρ,τ,σ$)-derivations of two-dimensional left-symmetric dialgebras

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 .

Paper Structure

This paper contains 4 sections, 3 theorems, 29 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. $(\rho, \tau, \sigma)$-Derivations of Left-Symmetric Dialgebras
  4. $(\rho, \tau, \sigma)$-Derivations of Low-Dimensional Left-Symmetric Dialgebras

Key Result

Proposition 3.2

Let $S$ be a complex left symmetric dialgebra. Then the values of $\rho, \tau, \sigma$ in $Der_{(\rho,\tau,\sigma)}S$ are distributed as follows: where $\ast=\dashv,\vdash$ denotes the operation in the left symmetric dialgebra.

Theorems & Definitions (15)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Remark 2.1
  • Example 2.4
  • Example 2.5
  • Definition 2.6
  • Definition 2.7
  • Definition 3.1
  • Proposition 3.2
  • ...and 5 more