Symmetry of symplectic derivation Lie algebras of free Lie algebras

TL;DR

This paper reveals a symmetry in the stable irreducible decomposition of symplectic derivation Lie algebras of free Lie algebras, linked to the first homology of surfaces.

Contribution

It uncovers a previously unknown symmetry in the structure of symplectic derivation Lie algebras related to surface topology.

Findings

Identifies a symmetry in the stable irreducible decomposition.

Connects the symmetry to the first homology of compact oriented surfaces.

Enhances understanding of the algebraic structure of symplectic derivations.

Abstract

We show that a certain symmetry exists in the stable irreducible decomposition of the Lie algebra consisting of symplectic derivations of the free Lie algebra generated by the first homology group of compact oriented surfaces.