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$δ$-biderivations of Virasoro related algebras

Chengkang Xu

Abstract

We determine all $δ$-biderivations for the Witt algebra, the Virasoro algebra, the $W$-algebras $W(a,b)$ and their universal central extensions $\widetilde W(a,b)$, and then give some applications.

$δ$-biderivations of Virasoro related algebras

Abstract

We determine all -biderivations for the Witt algebra, the Virasoro algebra, the -algebras and their universal central extensions , and then give some applications.
Paper Structure (13 sections, 21 theorems, 119 equations)

This paper contains 13 sections, 21 theorems, 119 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Basic properties of $\delta$-biderivations
  4. $\delta$-biderivations of the Witt and Virasoro algebras
  5. $\delta$-biderivations of the Witt algebra
  6. $\delta$-biderivations of the Virasoro algebra
  7. $\delta$-biderivations of the $W$-algebras
  8. $\delta$-biderivations of $W(a,b)$
  9. $\delta$-biderivations of $\widetilde{W}(a,b)$
  10. Applications
  11. Commuting linear maps
  12. Commutative post-Lie algebra
  13. Transposed $\delta$-Poisson algebra structure

Key Result

Theorem 2.3

The algebra $\widetilde{W}(a,b)$ satisfies the following Lie brackets where $C_0,C_1^{0},C_1^{1},C_2^{1},C_1^{-1},C_2^0,C_2^{\frac{1}{2},0}$ are central elements.

Theorems & Definitions (46)

  • Definition 2.1
  • Definition 2.2
  • Theorem 2.3
  • Definition 2.4
  • Theorem 2.5: KKS
  • Definition 2.6
  • Proposition 3.1
  • proof
  • Proposition 3.2
  • proof
  • ...and 36 more