Differential Gerstenhaber algebras associated to nilpotent algebras

Details Differential Gerstenhaber algebras associated to nilpotent algebras Differential Gerstenhaber algebras associated to nilpotent algebras

2007-08-25

arxiv.org/abs/0708.3442v2

Mathematics

Algebraic Geometry

30 Pages. 3 Tables. Proof of Theorem 29 is revised. Other minor edits

Scientific paper

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-K\"ahlerian 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-K\"ahler structures on six-dimensional nilpotent algebras whose mirror images are themselves.

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