The symmetric operation in a free pre-Lie algebra is magmatic

DOI10.1090/S0002-9939-2010-10813-4zbMath1264.17001arXiv1004.1204WikidataQ115289292 ScholiaQ115289292MaRDI QIDQ3003571

Nantel Bergeron, Jean-Louis Loday

Publication date: 27 May 2011

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

Full work available at URL: https://arxiv.org/abs/1004.1204

zbMATH Keywords

dendriform algebraspre-Lie algebrasoperadsduplicial algebrascommutative magmatic algebras

Mathematics Subject Classification ID

Trees (05C05) Nonassociative algebras satisfying other identities (17A30)

Related Items (8)

Jordan trialgebras and post-Jordan algebras ⋮ Graph insertion operads ⋮ Gröbner-Shirshov bases for free Gelfand-Dorfman-Novokov algebras and for right ideals of free right Leibniz algebras ⋮ Polynomial identities of bicommutative algebras, Lie and Jordan elements ⋮ Algebraic structures of \(F\)-manifolds via pre-Lie algebras ⋮ The Lie algebra of classical mechanics ⋮ Fine structures inside the PreLie operad ⋮ On the commutator in Leibniz algebras

Cites Work

• Shuffle bialgebras.
• Eulerian idempotents and Milnor-Moore theorem for certain non-cocommutative Hopf algebras
• The non-symmetric operad pre-Lie is free
• A rigidity theorem for pre-Lie algebras
• Algebraic Operads
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