Alg\`ebres enveloppantes \`a homotopie pr\`es, homologie et cohomologie

TL;DR

This paper introduces a unified framework for homology and cohomology theories across various algebraic structures, emphasizing the role of symmetries and differentials in their construction.

Contribution

It provides a novel unified approach to algebraic homology and cohomology, integrating associative, commutative, Lie, and Gerstenhaber algebras under a common framework.

Findings

Unified construction for various algebraic homologies and cohomologies

Distinction between linear parts and structure-induced differentials

Applicable to associative, commutative, Lie, and Gerstenhaber algebras

Abstract

We present an unified construction for algebras and modules homologies and cohomologies, in the case of associative, commuttaive, Lie and Gerstenhaber algebras. We make a distinction between the linear part of the construction of algebras and cogebras, characterized by the symmetries of the defining relations and the structure itself which appears as a differential on these algebras and cogebras.