Eulerian idempotents and Milnor-Moore theorem for certain non-cocommutative Hopf algebras

The purpose of this paper is to prove a Milnor-Moore style theorem for a particular kind of non-cocommutative Hopf algebras: the dendriform algebras. A dendriform Hopf algebra is a Hopf algebra, such that the product * is the sum of two operations ≺ and ≻, verifying certain conditions between them a...

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Autor principal: Ronco, M.
Formato: JOUR
Materias:
Dendriform algebra
Hopf algebra
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00218693_v254_n1_p152_Ronco
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00218693_v254_n1_p152_Ronco2023-10-03T14:21:19Z Eulerian idempotents and Milnor-Moore theorem for certain non-cocommutative Hopf algebras Ronco, M. Dendriform algebra Hopf algebra The purpose of this paper is to prove a Milnor-Moore style theorem for a particular kind of non-cocommutative Hopf algebras: the dendriform algebras. A dendriform Hopf algebra is a Hopf algebra, such that the product * is the sum of two operations ≺ and ≻, verifying certain conditions between them and with the coproduct Δ. The role of Lie algebras is played by brace algebras, which are defined by n-ary operations (one for each n ≥ 2) satisfying some relations. We show that a dendriform Hopf algebra is isomorphic to the enveloping algebra of its brace algebra of primitive elements. One of the ingredients of the proof is the construction of Eulerian idempotents in this context. © 2002 Elsevier Science (USA). All rights reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00218693_v254_n1_p152_Ronco
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Dendriform algebra
Hopf algebra
spellingShingle Dendriform algebra
Hopf algebra
Ronco, M.
Eulerian idempotents and Milnor-Moore theorem for certain non-cocommutative Hopf algebras
topic_facet Dendriform algebra
Hopf algebra
description The purpose of this paper is to prove a Milnor-Moore style theorem for a particular kind of non-cocommutative Hopf algebras: the dendriform algebras. A dendriform Hopf algebra is a Hopf algebra, such that the product * is the sum of two operations ≺ and ≻, verifying certain conditions between them and with the coproduct Δ. The role of Lie algebras is played by brace algebras, which are defined by n-ary operations (one for each n ≥ 2) satisfying some relations. We show that a dendriform Hopf algebra is isomorphic to the enveloping algebra of its brace algebra of primitive elements. One of the ingredients of the proof is the construction of Eulerian idempotents in this context. © 2002 Elsevier Science (USA). All rights reserved.
format JOUR
author Ronco, M.
author_facet Ronco, M.
author_sort Ronco, M.
title Eulerian idempotents and Milnor-Moore theorem for certain non-cocommutative Hopf algebras
title_short Eulerian idempotents and Milnor-Moore theorem for certain non-cocommutative Hopf algebras
title_full Eulerian idempotents and Milnor-Moore theorem for certain non-cocommutative Hopf algebras
title_fullStr Eulerian idempotents and Milnor-Moore theorem for certain non-cocommutative Hopf algebras
title_full_unstemmed Eulerian idempotents and Milnor-Moore theorem for certain non-cocommutative Hopf algebras
title_sort eulerian idempotents and milnor-moore theorem for certain non-cocommutative hopf algebras
url http://hdl.handle.net/20.500.12110/paper_00218693_v254_n1_p152_Ronco
work_keys_str_mv AT roncom eulerianidempotentsandmilnormooretheoremforcertainnoncocommutativehopfalgebras
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