Biderivations of the higher rank Witt algebra without anti-symmetric condition

Abstract

The Witt algebra 𝔚d of rank d(≥ 1) is the derivation algebra of Laurent polynomial algebras in d commuting variables. In this paper, all biderivations of 𝔚d without anti-symmetric condition are determined. As an applications, commutative post-Lie algebra structures on 𝔚d are obtained. Our conclusions recover and generalize results in the related papers on low rank or anti-symmetric cases.

Keywords

• biderivation
• higher rank witt algebra
• anti-symmetric
• post-lie algebra
• 17b05
• 17b40