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