Deformation quantization of non associative algebras

TL;DR

This paper explores the process of deformation quantization applied to nonassociative algebras, including Leibniz algebras, focusing on their associator properties and applying polarization-depolarization techniques.

Contribution

It extends deformation quantization methods to a broader class of nonassociative algebras, particularly Leibniz algebras, and introduces polarization-depolarization procedures.

Findings

Deformation quantization applied to nonassociative algebras with symmetric associator relations.

Extension of quantization techniques to Leibniz algebras.

Application of polarization-depolarization rule to this class.

Abstract

We study deformation quantization of nonassociative algebras whose associator satisfies some symmetric relations. This study is expanded to a larger class of nonassociative algebras includind Leibniz algebras. We apply also to this class the rule of polarization-depolarization.