Algebraic Investigation of the Soft Seven Sphere

TL;DR

This paper explores the seven sphere as a soft Lie algebra with structure functions, explicitly calculating these functions and examining key properties like Jacobi identities and algebraic consistency.

Contribution

It provides the first explicit calculation of structure functions for the soft seven sphere and analyzes its algebraic properties and consistency conditions.

Findings

Explicit structure functions for the soft seven sphere are derived.

The validity of Jacobi identities in this context is discussed.

Key features like pointwise reduction and closure are confirmed.

Abstract

We investigate the seven sphere as a soft Lie algebra i.e. an algebra with structure functions instead of structure constants. We calculate its structure functions explicitly and also discuss some relevant points such as the validity of the Jacobi identities. Furthermore, we emphasis some important features such as the pointwise reduction, closure and some other consistency checks.