Twisted descent algebras and the Solomon-Tits algebra.

DOI10.1016/j.aim.2005.01.010zbMath1154.16029arXivmath/0310310OpenAlexW2047773592MaRDI QIDQ2576999

Manfred Schocker, Frédéric Patras

Publication date: 29 December 2005

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0310310

zbMATH Keywords

tensor speciestwisted algebrasdescent algebrasshufflespeak algebrastwisted bialgebras

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Hecke algebras and their representations (20C08) Representations of finite symmetric groups (20C30)

Related Items

The module structure of the Solomon-Tits algebra of the symmetric group. ⋮ Twisted pre-Lie algebras of finite topological spaces ⋮ The \((1-\mathbb{E})\)-transform in combinatorial Hopf algebras ⋮ Doubling twisted pre-Lie algebras of finite topological spaces ⋮ Nonlocal, noncommutative diagrammatics and the linked cluster theorems ⋮ Shuffle bialgebras. ⋮ Strong forms of linearization for Hopf monoids in species ⋮ Symmetril Moulds, Generic Group Schemes, Resummation of MZVs ⋮ Lie Theory for Quasi-Shuffle Bialgebras ⋮ A theory of pictures for quasi-posets ⋮ Natural endomorphisms of quasi-shuffle Hopf algebras ⋮ Strong forms of self-duality for Hopf monoids in species ⋮ A quiver presentation for Solomon's descent algebra. ⋮ Trees, set compositions and the twisted descent algebra

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The peak algebra and the Hecke-Clifford algebras at \(q=0\)
• Adams operations, iterated integrals and free loop spaces cohomology
• On Dynkin and Klyachko idempotents in graded bialgebras
• The module structure of the Solomon-Tits algebra of the symmetric group.
• The equivalence of certain categories of twisted Lie and Hopf algebras over a commutative ring
• Buildings of spherical type and finite BN-pairs
• A Mackey formula in the group of a Coxeter group. With an appendix by J. Tits: Two properties of Coxeter complexes
• Hopf algebra of the planar binary trees
• Hopf algebras, renormalization and noncommutative geometry
• The weight decomposition of Hopf algebras
• The descent algebra of a graded bialgebra
• Shifted quasi-symmetric functions and the Hopf algebra of peak functions
• Peak quasisymmetric functions and Eulerian enumeration
• The peak algebra of the symmetric group
• Adams operations, algebras up to homotopy and cyclic homology
• Semigroups, rings, and Markov chains
• The peak algebra of the symmetric group revisited.
• Noncommutative symmetric functions
• Double shuffles of multiple polylogarithms at roots of unity
• Lie representations and an algebra containing Solomon's.
• Duality between quasi-symmetric functions and the Solomon descent algebra
• A combinatorial description of the spectrum for the Tsetlin library and its generalization to hyperplane arrangements
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• Noncommutative Symmetric Functions II: Transformations of Alphabets
• The peak algebra and the descent algebras of types B and D
• Renormalization
• Enriched 𝑃-Partitions
• Combinatoric explosion of renormalization tamed by Hopf algebra: 30-loop Padé-Borel resummation.
• Renormalization of QED with planar binary trees
• Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The \(\beta\)-function, diffeomorphisms and the renormalization group.
• Collected papers of K. -T. Chen. Edited by Philippe Tondeur