On the (co)homology of the partition lattice and the free Lie algebra. (Q1584469)
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scientific article; zbMATH DE number 1525039
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the (co)homology of the partition lattice and the free Lie algebra. |
scientific article; zbMATH DE number 1525039 |
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On the (co)homology of the partition lattice and the free Lie algebra. (English)
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2 November 2000
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We explore the well-known relationship between the representations of the symmetric group on the homology of the partition lattice and on the \(l^n\) component of the free Lie algebra. We give two new combinatorial proofs of the sign twisted isomorphism between the two modules. One involves a bijection between bases and the other involves a bijection between generating sets which takes relations to relations.
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symmetric group
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partition lattice
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free Lie algebra
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0.8976236
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0.89581114
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0.8890986
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0.88766235
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