The Solvabilizers and Solvable Graphs in Lie Superalgebras

In this paper, we introduce the solvabilizer and the solvable graph for a Lie superalgebra and establish their basic properties. Then we define a category which links Lie superalgebras to their solvable substructures. Afterwards, we prove that the solvable graph is one of the isomorphic invariants of the Lie superalgebras. Furthermore, we introduce the solvability measure, which can reflect the degree of solvability of Lie superalgebras.