2025/08/14 by Ivan Kaygorodov, Abror Khudoyberdiyev, Kaygorodov, Ivan +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2508.14914
openalex publication_date 2025/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present work, we compute quasi-derivations of the Witt algebra and some algebras well-related to the Witt algebra. Namely, we prove that each quasi-derivation of the Witt algebra is a sum of a derivation and a (1)/(2)-derivation; a similar result is obtained for the Virasoro algebra. A different situation appears for Lie algebras \mathcal W(a,b): in the case of b=-1, they do not have interesting examples of quasi-derivations, but the case of b≠-1 provides some new non-trivial examples of quasi-derivations. We also completely describe all quasi-derivations of \mathcal W(a,b). As a corollary, we describe the derivations and quasi-derivations of the Novikov-Witt and admissible Novikov-Witt algebras previously constructed by Bai and his co-authors; and δ-derivations and transposed δ-Poisson structures on cited Lie algebras. In particular, we proved that each \mathcal W(a,b) admits a nontrivial transposed \frac 11-b-Poisson structure.