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The Solvabilizers and Solvable Graphs in Lie Superalgebras

Baojin Zhang, Liming Tang

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.

The Solvabilizers and Solvable Graphs in Lie Superalgebras

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.
Paper Structure (3 sections, 16 theorems, 49 equations)

This paper contains 3 sections, 16 theorems, 49 equations.

Table of Contents

  1. Basic
  2. The solvabilizer of a Lie superalgebra
  3. The Solvable Graph of Lie Superalgebras

Key Result

Proposition 3

Suppose that $L$ is a Lie superalgebra and $A,B,C$ are non-empty subsets of $L$. Then the following properties hold:

Theorems & Definitions (38)

  • Definition 1
  • Example 2
  • Proposition 3
  • proof
  • Theorem 4
  • proof
  • Theorem 5
  • proof
  • Theorem 6
  • proof
  • ...and 28 more