The Solvabilizers and Solvable Graphs in Lie Superalgebras

TL;DR

This paper introduces the concepts of solvabilizer and solvable graph for Lie superalgebras, establishing their properties and invariants, and defines a solvability measure to quantify the degree of solvability.

Contribution

It presents new structures and invariants for Lie superalgebras, linking them to their solvable substructures and providing a measure of solvability.

Findings

Solvable graph is an isomorphic invariant of Lie superalgebras.

Defined a solvability measure reflecting the degree of solvability.

Established basic properties of solvabilizer and solvable graph.

Abstract

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.