The module structure of the Solomon-Tits algebra of the symmetric group.

DOI10.1016/j.jalgebra.2005.07.032zbMath1155.20012arXivmath/0505137OpenAlexW2072651951MaRDI QIDQ855707

Manfred Schocker

Publication date: 7 December 2006

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

Full work available at URL: https://arxiv.org/abs/math/0505137

zbMATH Keywords

symmetric groupsfree Lie algebrassemigroup algebrasprincipal indecomposable modulesCartan invariantsfinite Coxeter systemsCoxeter complexesset compositionsSolomon algebrasdescending Loewy seriesSolomon-Tits algebrastwisted descent algebras

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Hecke algebras and their representations (20C08) Representations of finite symmetric groups (20C30) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Semigroup rings, multiplicative semigroups of rings (20M25)

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Quivers of monoids with basic algebras, Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometry, The \((1-\mathbb{E})\)-transform in combinatorial Hopf algebras, Face monoid actions and tropical hyperplane arrangements, On the quiver of the descent algebra., Natural endomorphisms of quasi-shuffle Hopf algebras, The quiver of an algebra associated to the Mantaci-Reutenauer descent algebra and the homology of regular semigroups., Subalgebras of Solomon's descent algebra based on alternating runs, A quiver presentation for Solomon's descent algebra., Trees, set compositions and the twisted descent algebra, On the decomposition map for symmetric groups., Twisted descent algebras and the Solomon-Tits algebra.

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