Deformations of graded Lie algebras and symplectic structures

Dmitri V. Millionschikov

paper

Deformations of graded Lie algebras and symplectic structures

arXiv:math/0305057

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

26 pages