The Orlik-Solomon algebra on the partition lattice and the free Lie algebra

DOI10.1016/0097-3165(90)90049-3zbMath0709.17004OpenAlexW2040054883WikidataQ115363924 ScholiaQ115363924MaRDI QIDQ921099

Hélène Barcelo, Nantel Bergeron

Publication date: 1990

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0097-3165(90)90049-3

zbMATH Keywords

free Lie algebrarepresentationOrlik-Solomon algebrasymmetric groupexterior algebrapartition lattice

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Representations of finite symmetric groups (20C30) Identities, free Lie (super)algebras (17B01)

Related Items (13)

On the free Lie algebra with multiple brackets ⋮ Cohomology of Coxeter arrangements and Solomon’s descent algebra ⋮ On the action of the symmetric group on the free Lie algebra and the partition lattice ⋮ Hopf algebras and Markov chains: two examples and a theory ⋮ A hyperoctahedral analogue of the free Lie algebra ⋮ On the (co)homology of the poset of weighted partitions ⋮ The \(h,k\)-equal partition lattice is EL-shellable when \(h \geq k\) ⋮ Spectra of Symmetrized Shuffling Operators ⋮ A decomposition of Solomon's descent algebra ⋮ Free Lie superalgebras, trees and chains of partitions ⋮ Cohomology of Dowling lattices and Lie (super)algebras ⋮ On the (co)homology of the partition lattice and the free Lie algebra. ⋮ Counting permutations with given cycle structure and descent set

Cites Work

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• On the action of the symmetric group on the free Lie algebra and the partition lattice
• On the action of the symmetric group on the cohomology of the complement of its reflecting hyperplanes
• Combinatorics and topology of complements of hyperplanes
• Some aspects of groups acting on finite posets
• Broken circuit complexes: Factorizations and generalizations
• A hyperoctahedral analogue of the free Lie algebra
• On the Poincaré Series Associated with Coxeter Group Actions on Complements of Hyperplanes
• On the Poincaré-Birkhoff-Witt theorem
• Free differential calculus. IV: The quotient groups of the lower central series

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