Lie representations and an algebra containing Solomon's.

DOI10.1023/A:1021856522624zbMath1056.16032OpenAlexW1546574518MaRDI QIDQ1863002

Christophe Reutenauer, Frédéric Patras

Publication date: 11 March 2003

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1021856522624

zbMATH Keywords

Hopf algebrasdescent algebrassymmetric group algebrasLie idempotents

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Representations of finite symmetric groups (20C30) Group rings of finite groups and their modules (group-theoretic aspects) (20C05)

Related Items (7)

Lie idempotent algebras. ⋮ Quadri-algebras, preLie algebras, and the Catalan family of Lie idempotents ⋮ Noncommutative symmetric functions. VII: Free quasi-symmetric functions revisited ⋮ Structure of the Malvenuto-Reutenauer Hopf algebra of permutations ⋮ The peak algebra of the symmetric group revisited. ⋮ An unpublished theorem of Manfred Schocker and the Patras-Reutenauer algebra ⋮ Twisted descent algebras and the Solomon-Tits algebra.

Cites Work

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• On some submodules of the action of the symmetric group on the free Lie algebra
• A Mackey formula in the group of a Coxeter group. With an appendix by J. Tits: Two properties of Coxeter complexes
• The descent algebra of a graded bialgebra
• Noncommutative symmetric functions
• Duality between quasi-symmetric functions and the Solomon descent algebra
• Higher Lie idempotents
• Orthogonal projection onto the free Lie algebra
• On the structure of Hopf algebras
• Noncommutative Symmetric Functions II: Transformations of Alphabets

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