2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140300This 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 such that the differential Gerstenhaber algebra of its complex structure is quasi-isomorphic to that of its symplectic structure. In a weak sense of mirror symmetry, it is a classification of pseudo-Kähler structures on six-dimensional nilpotent algebras whose mirror images are themselves.30 Pages. 3 Tables. Proof of Theorem 29 is revised. Other minor editsAlgebraic GeometryMathematical PhysicsDifferential Geometry32G05 (Primary) 32G07, 53D45 (Secondary)text