Asian Journal of Mathematics

Volume 12 (2008)

Number 2

Differential Gerstenhaber Algebras Associated to Nilpotent Algebras

Pages: 225 – 250



Richard Cleyton

Yat-Sun Poon


This article provides a complete description of the differential Gerstenhaber algebras of all nilpotent complex structures on any real six-dimensional nilpotent algebra. As an application, we classify all pseudo-Kählerian complex structures on six-dimensional nilpotent algebras whose differential Gerstenhaber algebra is quasi-isomorphic to that of the symplectic structure. In a weak sense of mirror symmetry, this gives a classification of pseudo-Kähler structures on six-dimensional nilpotent algebras whose mirror images are themselves.


Nilpotent algebra; Gerstenhaber algebra; complex structure; symplectic structure; deformation; mirror symmetry

2010 Mathematics Subject Classification

Primary 32G05. Secondary 13D10, 16E45, 17B30, 32G07, 53D45.

Published 1 January 2008