Asian Journal of Mathematics

Volume 18 (2014)

Number 2

Differential Gerstenhaber algebras of generalized complex structures

Pages: 191 – 218

DOI: http://dx.doi.org/10.4310/AJM.2014.v18.n2.a1

Authors

Daniele Grandini (Department of Mathematics, University of California at Riverside)

Yat-Sun Poon (Department of Mathematics, University of California at Riverside)

Brian Rolle (Department of Mathematics, University of California at Riverside)

Abstract

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.

Keywords

DGA, generalized complex, holomorphic Poisson, nilmanifolds

2010 Mathematics Subject Classification

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

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