Asian Journal of Mathematics
Volume 12 (2008)
Differential Gerstenhaber Algebras Associated to Nilpotent Algebras
Pages: 225 – 250
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.