On the $\pd$- and $\barpd$-Operators of a Generalized Complex Structure

TL;DR

This paper establishes the equivalence between two sets of operators, the - and -operators from generalized complex geometry and the - and -operators from Lie bialgebroid modules, unifying different frameworks.

Contribution

It proves the operators introduced in generalized complex structures are identical to those in Lie bialgebroid modules, connecting two mathematical theories.

Findings

- and -operators coincide with - and -operators.

The equivalence unifies frameworks in generalized complex geometry and Lie bialgebroid theory.

Provides a bridge between different mathematical structures.

Abstract

In this note, we prove that the $\pd$- and $\barpd$-operators introduced by Gualtieri for a generalized complex structure coincide with the $\bdees$- and $\bdel$-operators introduced by Alekseev-Xu for Evens-Lu-Weinstein modules of a Lie bialgebroid.