Asian Journal of Mathematics
- Asian J. Math.
- Volume 12, Number 2 (2008), 225-250.
Differential Gerstenhaber Algebras Associated to Nilpotent Algebras
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.
Asian J. Math., Volume 12, Number 2 (2008), 225-250.
First available in Project Euclid: 9 September 2008
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 32G05: Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15]
Secondary: 32G07: Deformations of special (e.g. CR) structures 13D10: Deformations and infinitesimal methods [See also 14B10, 14B12, 14D15, 32Gxx] 16E45: Differential graded algebras and applications 17B30: Solvable, nilpotent (super)algebras 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]
Cleyton, Richard; Poon, Yat-Sun. Differential Gerstenhaber Algebras Associated to Nilpotent Algebras. Asian J. Math. 12 (2008), no. 2, 225--250. https://projecteuclid.org/euclid.ajm/1220986066