Abelian Hypercomplex 8-Dimensional Nilmanifolds

By I. Dotti, Anna Fino. 2000

54 citations recorded by the source corpus.

We study invariant Abelian hypercomplex structures on 8-dimensional nilpotent Lie groups. We prove that a group N admitting such a structure is either Abelian or an Abelian extension of a group of type H. We determine the Poincaré polynomials of the associated nilmanifolds and study the existence of symplectic and quaternionic structures on such spaces.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c72af38c18767c957951c2f9229bccdffb0efbc9

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Deformation of 2‐Step Nilmanifolds with Abelian Complex Structures (2004, background): “This concept was first considered in [5], and plays a fundamental role in the study of complex structures on solvable Lie groups [3, 4], turning out to be especially important in hypercomplex and HKT geometry [2, 9, 10, 14].”
A correction to “Tamed symplectic forms and strong Kähler with torsion metrics” (2012, background): “In particular, by [8] there exist only three (non-abelian) nilpotent Lie algebras of dimension 8 admitting an abelian hypercomplex structure and they are abelian extensions of a Lie algebra of Heinsenberg type, i.”
Complex product structures on Lie algebras (2003, background): “A classification of 8-dimensional nilpotent Lie groups carrying an abelian hypercomplex structure (meaning all its complex structures satisfy (24)) was given in [12].”
Properties of manifolds with skew-symmetric torsion and special holonomy (2004, background): “If we restrict to the 8-dimensional case all simply connected nilpotent Lie groups which carry invariant abelian hypercomplex structures are described in [9].”