Deformations of graded Lie algebras and symplectic structures

Dmitri V. Millionschikov

Deformations of graded Lie algebras and symplectic structures

Rings and Algebras 2007-05-23 v1 Symplectic Geometry

Authors: Dmitri V. Millionschikov

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: $[e_i,e_j]=(j-i)e_{i+j}+\sum_{l{=}1}c_{ij}^l e_{i+j+l}, i+j \le n.$ In even dimensions the subspace of symplectic Lie algebras has the codimension one.

Keywords

filiform lie algebras symplectic structures nilpotent lie algebras deformations graded lie algebras classification

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@article{arxiv.math/0305057,
  title  = {Deformations of graded Lie algebras and symplectic structures},
  author = {Dmitri V. Millionschikov},
  journal= {arXiv preprint arXiv:math/0305057},
  year   = {2007}
}

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26 pages

Deformations of graded Lie algebras and symplectic structures

Abstract

Keywords

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