Deformation Theory of Courant Algebroids via the Rothstein Algebra

TL;DR

This paper develops an algebraic framework for Courant algebroids, explores their deformation theory using graded Poisson algebras, and proposes initial steps towards their quantization via Fedosov-like methods.

Contribution

It introduces a purely algebraic definition of Courant algebroids and studies their deformation theory using two equivalent graded Poisson algebras, also proposing a quantization approach.

Findings

Defined Courant algebroids algebraically

Studied their deformation via graded Poisson algebras

Proposed a Fedosov-like quantization method

Abstract

In this paper we define Courant algebroids in a purely algebraic way and study their deformation theory by using two different but equivalent graded Poisson algebras of degree -2. First steps towards a quantization of Courant algebroids are proposed by employing a Fedosov like deformation quantization.