2002/05/06 by Dmitri V. Millionschikov, Millionschikov, Dmitri V.
Mathematics · #17B30 #17B56 #17B70 #53D #Differential Geometry (math.DG) #FOS: Mathematics #Rings and Algebras (math.RA) #Symplectic Geometry (math.SG) #math.DG #math.RA #math.SG #msc:17B30 #msc:17B56 #msc:17B70 #msc:53D
paper · pdf · doi:10.48550/arxiv.math/0205042
20 pages
arxiv created 2002/05/06 · arxiv updated 2009/11/30
We study symplectic (contact) structures on nilmanifolds that correspond to the filiform Lie algebras - nilpotent Lie algebras of the maximal length of the descending central sequence. We give a complete classification of filiform Lie algebras that possess a basis e1, ..., en, [ei,ej]=cije_i+j (N-graded Lie algebras). In particular we describe the spaces of symplectic cohomology classes for all even-dimensional algebras of the list. It is proved that a symplectic filiform Lie algebra is a filtered deformation of some N-graded symplectic filiform Lie algebra. But this condition is not sufficient. A spectral sequence is constructed in order to answer the question whether a given deformation of a N-graded symplectic filiform Lie algebra admits a symplectic structure or not. Other applications and examples are discussed.