Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A super Version of a Theorem of Fricke and Klein

Marcel Dang

Abstract

We start studying the character variety of the algebraic supergroup OSp(1|2) from the algebraic perspective. We do this by first investigating the specific case of the character variety of the free group on two letters and try to describe the ring of invariants with respect to the conjugation action. The explicit description of the corresponding character variety for SL(2) was done by Fricke and Klein, so this can be seen as a variant of this theorem for its supergeometric counterpart OSp(1|2).

A super Version of a Theorem of Fricke and Klein

Abstract

We start studying the character variety of the algebraic supergroup OSp(1|2) from the algebraic perspective. We do this by first investigating the specific case of the character variety of the free group on two letters and try to describe the ring of invariants with respect to the conjugation action. The explicit description of the corresponding character variety for SL(2) was done by Fricke and Klein, so this can be seen as a variant of this theorem for its supergeometric counterpart OSp(1|2).
Paper Structure (9 sections, 20 theorems, 115 equations)

This paper contains 9 sections, 20 theorems, 115 equations.

Table of Contents

  1. Introduction
  2. Fricke-Klein
  3. Preliminaries
  4. Supergeometry
  5. Supergroups
  6. V
  7. Invariant Theory
  8. Character Varieties
  9. Main Result

Key Result

Theorem 1.1

The $\operatorname{OSp}(V)$-invariant polynomial functions (by conjugation) on $\operatorname{OSp}(V) \times \operatorname{OSp}(V)$ are generated by 7 traces.

Theorems & Definitions (75)

  • Theorem 1.1
  • Lemma 2.1
  • proof
  • Remark 2.2
  • Theorem 2.3
  • proof
  • Definition 3.1
  • Definition 3.2
  • Remark 3.3
  • Example 3.4
  • ...and 65 more