Asian Journal of Mathematics

Differential Gerstenhaber Algebras Associated to Nilpotent Algebras

Richard Cleyton and Yat-Sun Poon

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Abstract

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.

Article information

Source
Asian J. Math., Volume 12, Number 2 (2008), 225-250.

Dates
First available in Project Euclid: 9 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1220986066

Mathematical Reviews number (MathSciNet)
MR2439262

Zentralblatt MATH identifier
1201.32008

Subjects
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]

Keywords
Nilpotent algebra Gerstenhaber algebra complex structure symplectic structure deformation mirror symmetry

Citation

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


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