Open Access
April 2014 Differential Gerstenhaber algebras of generalized complex structures
Daniele Grandini, Yat-Sun Poon, Brian Rolle
Asian J. Math. 18(2): 191-218 (April 2014).


Associated to every generalized complex structure is a differential Gerstenhaber algebra (DGA). When the generalized complex structure deforms, so does the associated DGA. In this paper, we identify the infinitesimal conditions when the DGA is invariant as the generalized complex structure deforms. We prove that the infinitesimal condition is always integrable. When the underlying manifold is a holomorphic Poisson nilmanifolds, or simply a group in the general, and the geometry is invariant, we find a general construction to solve the infinitesimal conditions under some geometric conditions. Examples and counterexamples of existence of solutions to the infinitesimal conditions are given.


Download Citation

Daniele Grandini. Yat-Sun Poon. Brian Rolle. "Differential Gerstenhaber algebras of generalized complex structures." Asian J. Math. 18 (2) 191 - 218, April 2014.


Published: April 2014
First available in Project Euclid: 27 August 2014

zbMATH: 1298.53083
MathSciNet: MR3217633

Primary: 53D18
Secondary: 16E45 , 22E25 , 32G05 , 53D17

Keywords: DGA , generalized complex , holomorphic Poisson , nilmanifolds

Rights: Copyright © 2014 International Press of Boston

Vol.18 • No. 2 • April 2014
Back to Top