Cohomology, Homotopy, Extensions, and Automorphisms of Nijenhuis Lie Conformal Algebras

2025/05/27 by Sania Asif, Asif, Sania · 2 citations
Mathematics · #14F35 #17B10 #17B38 #17B65 #17B69 #18N10 #18N40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2505.20867

openalex publication_date 2025/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper explores various algebraic and homotopical aspects of Nijenhuis Lie conformal algebras, including their cohomology theory, L_∞-structures, non-abelian extensions, and automorphism groups. We define the cohomology of a Nijenhuis Lie conformal algebra and relate it to the deformation theory of such structures. We also introduce 2-term Nijenhuis L_∞-conformal algebras and establish their correspondence with crossed modules and 3-cocycles in the cohomology of Nijenhuis Lie conformal algebras. Furthermore, we develop a classification theory for non-abelian extensions of Nijenhuis Lie conformal algebras via the second non-abelian cohomology group. Finally, we study the inducibility problem for automorphisms under such extensions, introducing a Wells-type map and deriving an associated exact sequence.

Cited by

• An embedding theorem for Nijenhuis Lie algebras
• Quasi-Twilled Lie Pseudolgebras and Their Deformation Maps

Related

• Deformation cohomology of Nijenhuis algebras and applications to extensions, inducibility of automorphisms and homotopy algebras
• Non-abelian cohomology of Nijenhuis Lie algebras and the inducibility of automorphisms and derivations
• Deformations of Nijenhuis Lie algebras and Nijenhuis Lie algebroids
• Cohomology theory of Nijenhuis Lie algebras and (generic) Nijenhuis Lie bialgebras
• Deformations and homotopy theory of Nijenhuis associative algebras