The module structure of Solomon's descent algebra

DOI10.1017/S1446788700036752zbMath1062.20010MaRDI QIDQ4805451

Dieter Blessenohl, Hartmut Laue

Publication date: 2002

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

free associative algebrasirreducible modulesprincipal indecomposable moduleslower central seriesdescending Loewy seriesPoincaré-Birkhoff-Witt basesSolomon descent algebrasCartan numbers

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Representations of finite symmetric groups (20C30) Identities, free Lie (super)algebras (17B01)

Related Items (10)

Lie idempotent algebras. ⋮ The module structure of the Solomon-Tits algebra of the symmetric group. ⋮ Representation theory of the higher-order peak algebras ⋮ Modular idempotents for the descent algebras of type A and higher Lie powers and modules ⋮ The \((1-\mathbb{E})\)-transform in combinatorial Hopf algebras ⋮ On the quiver presentation of the descent algebra of the symmetric group. ⋮ Cyclotomic Solomon algebras. ⋮ On the quiver of the descent algebra. ⋮ The peak algebra of the symmetric group revisited. ⋮ A quiver presentation for Solomon's descent algebra.

Cites Work

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• A decomposition of Solomon's descent algebra
• A Mackey formula in the group of a Coxeter group. With an appendix by J. Tits: Two properties of Coxeter complexes
• Noncommutative symmetric functions
• On the descending Loewy series of Solomon's descent algebra
• Central chains of ideals in an associative ring
• Solomon's Descent Algebra Revisited

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