The operators ∂ and ∂ of a generalized complex structure

Zhuo Chen

Vol. 242 (2009), No. 1, 53–69

DOI: 10.2140/pjm.2009.242.53

Abstract

We prove that the ∂ and ∂ operators introduced by Gualtieri for a generalized complex structure coincide with the d_∗ and ∂ operators introduced by Alekseev and Xu for Evens–Lu–Weinstein modules of a Lie bialgebroid.

Keywords

generalized complex structure, Lie bialgebroid, modular cocycle

Mathematical Subject Classification 2000

Primary: 53C15, 53D17, 57R15, 58A10

Secondary: 15A66, 17B63, 17B66

Milestones

Received: 2 December 2008

Revised: 15 April 2009

Accepted: 8 May 2009

Published: 1 September 2009