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Linear super-commuting maps and super-biderivations on Hom-lie superalgebras

Ashutosh Pandey

Abstract

This paper investigates the fundamental connections between linear super-commuting maps, super-biderivations, and centroids in Hom-Lie superalgebras under certain conditions. Our work generalizes the results of Bresar and Zhao on Lie algebras.

Linear super-commuting maps and super-biderivations on Hom-lie superalgebras

Abstract

This paper investigates the fundamental connections between linear super-commuting maps, super-biderivations, and centroids in Hom-Lie superalgebras under certain conditions. Our work generalizes the results of Bresar and Zhao on Lie algebras.

Paper Structure

This paper contains 4 sections, 12 theorems, 81 equations.

Table of Contents

  1. Introduction
  2. Notations and definitions
  3. Super-biderivations
  4. Linear super-commuting maps

Key Result

Lemma 3.1

Let $H$ be a Hom-Lie superalgebra and $d: H \to H$ be a linear super-commuting map. Assume Then $\phi: H \times H \to H$ is a super-biderivation.

Theorems & Definitions (24)

  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • Lemma 3.4
  • proof
  • Lemma 3.5
  • proof
  • ...and 14 more