Deformations of filiform Lie algebras and symplectic structures |
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Authors: | D V Millionshchikov |
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Institution: | (1) Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119992, Russia |
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Abstract: | 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
. For even n, the subspace of symplectic Lie algebras is determined by a single linear equation.
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2006, Vol. 252, pp. 194–216. |
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Keywords: | |
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