Deformations of filiform Lie algebras and symplectic structuresстатья
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Дата последнего поиска статьи во внешних источниках: 28 мая 2015 г.
Аннотация:We study symplectic structures on filiform Lie algebras, which are niplotent Lie algebras with the maximal length of the descending central sequence. Let g be a symplectic filiform Lie algebra and dim g = 2k ≥ 12. Then g is isomorphic to some ℕ-filtered deformation either of m0(2k) (defined by the structure relations [e 1, e i ] = e i+1, i = 2,…, 2k − 1) or of V 2k , the quotient of the positive part of the Witt algebra W + by the ideal of elements of degree greater than 2k. We classify ℕ-filtered deformations of V n : [e i , e j ] = (j − i)e i+1 + Σ l≥1 c ij l e i+j+l . For dim g = n ≥ 16, the moduli space ℳn of these deformations is the weighted projective space $\mathbb{K}P^4 \left( {n - 11,n - 10,n - 9,n - 8,n - 7} \right)$ . For even n, the subspace of symplectic Lie algebras is determined by a single linear equation.