Central extensions, derivations, and automorphisms of semi-direct sums of the Witt algebra with its intermediate series modules

2024/07/20 by Lucas Buzaglo, Girish S. Vishwa, Buzaglo, Lucas +1
Mathematics · #17B40 #17B56 (Primary) #17B65 #17B68 (Secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2407.14809

openalex publication_date 2024/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Lie algebras formed via semi-direct sums of the Witt algebra Der(ℂ[t,t^-1]) and its modules have become increasingly prominent in both physics and mathematics in recent years. In this paper, we complete the study of (Leibniz) central extensions, derivations and automorphisms of the Lie algebras formed from the semi-direct sum of the Witt algebra and its indecomposable intermediate series modules (that is, graded modules with one-dimensional graded components). Our techniques exploit the internal grading of the Witt algebra, which can be applied to a wider class of graded Lie algebras.

Related

• Simple Lie algebras which generalize Witt algebras
• Post-Lie algebra structures on the Witt algebra
• The derivations, central extensions and automorphism group of the Lie algebra W
• On structure of graded restricted simple Lie algebras of Cartan type as modules over the Witt algebra
• Quasi-hom-Lie Algebras, Central Extensions and 2-cocycle-like Identities