On the Leibniz (co)homology of the Lie algebra of the Euclidean group (Q534013)
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scientific article; zbMATH DE number 5886348
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Leibniz (co)homology of the Lie algebra of the Euclidean group |
scientific article; zbMATH DE number 5886348 |
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On the Leibniz (co)homology of the Lie algebra of the Euclidean group (English)
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10 May 2011
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The isometries of \(\mathbb R^n\) form the Euclidean group \(E(n)\). Via the identification of certain orthogonal invariants its Leibniz homology is shown to be isomorphic as a graded vector space to \[ (R\oplus < \alpha_n >) \oplus T^{*} (\gamma_n ) \] where \(\alpha\), has degree \(n, \gamma_n\) has degree \(n - 1\), and \(T^{*}\) denotes the tensor algebra functor. Dually the cohomology is determined. The methods here are an improvement on those used by \textit{J. M. Lodder} in [J. Lie Theory 18, No. 4, 897--914 (2008; Zbl 1171.17006)].
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