\(T_{\theta}^{\ast}\)-extensions of \(n\)-Lie algebras (Q643162)
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scientific article; zbMATH DE number 5964865
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(T_{\theta}^{\ast}\)-extensions of \(n\)-Lie algebras |
scientific article; zbMATH DE number 5964865 |
Statements
\(T_{\theta}^{\ast}\)-extensions of \(n\)-Lie algebras (English)
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28 October 2011
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Summary: The paper is mainly concerned with \(T_{\theta}^{\ast}\)-extensions of \(n\)-Lie algebras. The \(T_{\theta}^{\ast}\)-extension \(L_{\theta}(L^{\ast})\) of an \(n\)-Lie algebra \(L\) by a cocycle \(\theta\) is defined, and a class of cocycles is constructed by means of linear mappings from an \(n\)-Lie algebra on to its dual space. Finally all \(T_{\theta}^{\ast}\)-extensions of \((n + 1)\)-dimensional \(n\)-Lie algebras are classified, and the explicit multiplications are given.
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