Asian Journal of Mathematics

Differential Gerstenhaber algebras of generalized complex structures

Daniele Grandini, Yat-Sun Poon, and Brian Rolle

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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.

Article information

Asian J. Math., Volume 18, Number 2 (2014), 191-218.

First available in Project Euclid: 27 August 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D18: Generalized geometries (à la Hitchin)
Secondary: 16E45: Differential graded algebras and applications 22E25: Nilpotent and solvable Lie groups 32G05: Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15] 53D17: Poisson manifolds; Poisson groupoids and algebroids

DGA generalized complex holomorphic Poisson nilmanifolds


Grandini, Daniele; Poon, Yat-Sun; Rolle, Brian. Differential Gerstenhaber algebras of generalized complex structures. Asian J. Math. 18 (2014), no. 2, 191--218.

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