Drinfel'd algebra deformations and the associahedra

TL;DR

This paper develops a cohomology framework for deforming Drinfel'd algebras, linking combinatorial structures of associahedra with algebraic derivations, advancing understanding of algebraic deformations.

Contribution

It introduces a novel cohomology theory for Drinfel'd algebra deformations, connecting combinatorial and algebraic perspectives.

Findings

Established a graded Lie algebra structure on associahedra cochains

Linked deformation theory with derivations on the bar construction

Provided tools for systematic deformation analysis of Drinfel'd algebras

Abstract

We construct a cohomology theory controlling the deformations of a general Drinfel'd algebra. The picture presented here has two sides -- the combinatorial one related with the fact of the existence of a graded Lie algebra structure on the simplicial cochain complex of the associahedra, and the algebraic one related with the algebra of derivations on the bar construction.