On cohomology of nilpotent symplectic Lie algebras of dim. \(\leq 6\) and deformation of those of dim. \(\leq 4\) (Q2911891)
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scientific article; zbMATH DE number 6075896
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On cohomology of nilpotent symplectic Lie algebras of dim. \(\leq 6\) and deformation of those of dim. \(\leq 4\) |
scientific article; zbMATH DE number 6075896 |
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3 September 2012
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nilpotent Lie algebra
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cohomology
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symplectic Lie algebra
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deformation
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On cohomology of nilpotent symplectic Lie algebras of dim. \(\leq 6\) and deformation of those of dim. \(\leq 4\) (English)
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The authors calculate dimensions of adjoint cohomologies for nilpotent Lie algebras (over a field \(k\) of characteristic 0) for dimensions \(\leq 6\), which have a symplectic structure.NEWLINENEWLINEAlso in this paper easy explicit calculations, which are connected with a construction of some deformation of some Lie algebras for dimensions \(\leq 4\), are given.NEWLINENEWLINEIt is necessary to note that the much more complete results about cohomologies of nilpotent Lie algebras (for dimensions \(\leq 7\)) have been published by \textit{L. Magnin} in 1995 (for dimensions \(\leq 6\) the answer does not depend on the field \(k\)). NEWLINENEWLINESee ps-file on the Internet: Adjoint and trivial cohomology tables for indecomposable nilpotent Lie algebras of dimension \(\leq 7\) over \(\mathbb C\). Online e-book, 2nd corrected edition 2007, \url{http://monge.u-bourgogne.fr/lmagnin/Magnin2.ps}.
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