2025/12/12 by Mohsen Ben Abdallah, Abdallah, Mohsen Ben, Marwa Ennaceur +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Nonlinear Waves and Solitons #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.2512.12093
We give a complete and rigorous classification of homogeneous weight 0 Rota--Baxter operators on the Block-type Witt algebra B(q), assuming the operator has integral degree (k,k') ∈ ℤ2. A key correction is established in the non+resonant regime q ≠ k' with k ≠ 0: the profile function g(i) = f(-k,i) must satisfy the nonlinear functional equation (i - j)g(i)g(j) = g(i+j+k')[(i + k' + q)g(i) - (j + k' + q)g(j)], which admits only constant, Kronecker-delta, or finite-support solutions. This excludes previously and erroneously claimed families such as non-constant polynomials, exponentials, or nontrivial periodic functions. In contrast, the resonant case q = k' exhibits full flexibility: any profile g is admissible, provided the operator is supported on the single line m = -k. The classification is cohomologically exhaustive for generic q (i.e., when H1(B(q),B(q)) = 0), and is applied to derive all homogeneous post-Lie structures and associated Lie algebra deformations.