2025/12/03 by Mohsen Ben Abdallah, Abdallah, Mohsen Ben, Marwa Ennaceur +1 · 1 citation
Mathematics · #17B56 #17B65 #17D25 #81R12 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #G.2.1 #Homotopy and Cohomology in Algebraic Topology #I.1.2 #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2512.04294
openalex publication_date 2025/12/03 · openalex created_date 2025/12/06 · openalex updated_date 2026/07/28
We classify all homogeneous odd (i.e., parity-reversing) Rota--Baxter operators of weight zero on the modified Witt-type Lie superalgebra W = ⟨ Lm, Gn ⟩m,n∈\Z. Our classification shows that nontrivial such operators are highly constrained: either g ≡ 0 and f is arbitrary, or g \not≡ 0 forces f ≡ 0, and g must take one of several rigid forms dictated by the integer shift k (necessarily odd when g(0) ≠ 0). We prove that every Rota--Baxter operator on W decomposes uniquely into even and odd homogeneous components; we restrict our attention to the odd case, which yields the full nontrivial structure. Furthermore, we show that all derivations of W are inner, that no Rota--Baxter operator on W is invertible, and we describe the induced super pre-Lie algebra structure together with its cohomological interpretation.