Keller admissible triples and Duflo theorem

TL;DR

This paper explores Keller admissible triples, demonstrating their role in establishing Gerstenhaber algebra isomorphisms between Hochschild cohomologies, and provides a new proof of the Duflo--Kontsevich theorem for finite-dimensional Lie algebras.

Contribution

It introduces Keller admissible triples and shows they induce Gerstenhaber algebra isomorphisms, offering a new proof of the Duflo--Kontsevich theorem.

Findings

Keller admissible triples induce Gerstenhaber algebra isomorphisms

A new proof of the Duflo--Kontsevich theorem for finite-dimensional Lie algebras

Establishment of connections between Hochschild cohomologies and admissible triples

Abstract

The present paper is devoted to the study of Keller admissible triples. We prove that a Keller admissible triple induces an isomorphism of Gerstenhaber algebras between the Hochschild cohomologies of direct-sum type of the pair of differential graded algebras bound to one another by the admissible triple. As an application, we give a new concrete proof of the Duflo--Kontsevich theorem for finite-dimensional Lie algebras.