Pro-Solvable Extensions of a generalized Positive Witt Algebra

This paper is devoted to the study of a natural generalization of the positive Witt algebra. We first show that the algebra under consideration can be realized as a mutation of the positive Witt algebra. We then construct its pro-solvable Lie extensions and analyze their structural properties. Moreover, we prove that these extensions constitute a family of complete pro-solvable Lie algebras.