arXiv math/03050572003-05-03math.RAmath.SG

Deformations of graded Lie algebras and symplectic structures

Dmitri V. Millionschikov

备注：: 26 pages

英文摘要：

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.

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