Co-Moufang deformations of the universal enveloping algebra of the algebra of traceless octonions

TL;DR

This paper proves that under certain conditions, deformations of the universal enveloping algebra of traceless octonions are necessarily coassociative and cocommutative, using graphical calculus in characteristic zero.

Contribution

It introduces a graphical calculus approach to show that Moufang identity-preserving deformations are trivial in the specified algebraic setting.

Findings

Deformations satisfying Moufang identities are coassociative and cocommutative.

Graphical calculus effectively proves deformation constraints.

Results hold over fields of characteristic zero.

Abstract

By means of graphical calculus we prove that, over fields of characteristic zero, any bialgebra deformation of the universal enveloping algebra of the algebra of traceless octonions satisfying the dual of the left and right Moufang identities must be coassociative and cocommutative.