Deformations of graded Lie algebras and symplectic structures

2003/05/03 by Dmitri V. Millionschikov, Millionschikov, Dmitri V.
Mathematics · #17B30 (Primary) 53D05 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #Symplectic Geometry (math.SG) #math.RA #math.SG #msc:17B30 #msc:53D05

paper · pdf · doi:10.48550/arxiv.math/0305057

26 pages

arxiv created 2003/05/03 · openalex publication_date 2003/05/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study symplectic structures on filiform Lie algebras -- nilpotent Lie algebras of the maximal length of the descending central sequence. In the present article we classify the Lie algebras with the structure relations of the following form: [e_i,e_j]=(j-i)e_i+j+∑_l=1c_ij^l e_i+j+l, i+j ≤ n. In even dimensions the subspace of symplectic Lie algebras has the codimension one.

Related

• Graded filiform Lie algebras and symplectic nilmanifolds
• Cohomology and deformations of the infinite dimensional filiform Lie algebra m₀
• A distinguished example of filiform deformation
• Nonfiliform characteristically nilpotent Lie algebras
• Symplectic structures on 2-step nilpotent Lie algebras