Homomorphisms between Solomon's descent algebras

DOI10.1016/S0021-8693(05)80042-0zbMath0770.20008OpenAlexW1996291448MaRDI QIDQ1204547

Christophe Reutenauer, Adriano M. Garsia, François Bergeron

Publication date: 29 March 1993

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0021-8693(05)80042-0

zbMATH Keywords

embeddinggroup algebraderivationssymmetric grouppermutationdescent setfree associative algebrasurjective homomorphismSolomon's descent algebra

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Representations of finite symmetric groups (20C30) Automorphisms and endomorphisms (16W20) Identities, free Lie (super)algebras (17B01) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Derivations, actions of Lie algebras (16W25) Symmetric groups (20B30) Subgroups of symmetric groups (20B35)

Related Items

Symmetric functions, noncommutative symmetric functions and quasisymmetric functions. II. ⋮ The peak algebra of the symmetric group ⋮ A decomposition of the descent algebra of the hyperoctahedral group. I, II ⋮ Representation theory of Mantaci-Reutenauer algebras. ⋮ Orthogonal idempotents in the descent algebra of \(B_ n\) and applications ⋮ A decomposition of the descent algebra of a finite Coxeter group ⋮ Symbolic manipulation for the study of the descent algebra of finite Coxeter groups ⋮ A generating set of Solomon's descent algebra ⋮ A decomposition of Solomon's descent algebra ⋮ A multiplication rule for the descent algebra of type \(D\) ⋮ An unpublished theorem of Manfred Schocker and the Patras-Reutenauer algebra ⋮ Around Solomon's descent algebras.

Cites Work

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• A decomposition of Solomon's descent algebra
• Lie elements and an algebra associated with shuffles
• Shuffles of permutations and the Kronecker product
• A Mackey formula in the group of a Coxeter group. With an appendix by J. Tits: Two properties of Coxeter complexes