A Milnor-Moore theorem for dendriform Hopf 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 purpose of this Note is to announce a Milnor-Moore style theorem for these algebras. The role of Lie algebras is played b...

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Publicado: 2001
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07644442_v332_n2_p109_Ronco
http://hdl.handle.net/20.500.12110/paper_07644442_v332_n2_p109_Ronco
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_07644442_v332_n2_p109_Ronco
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spelling paper:paper_07644442_v332_n2_p109_Ronco2023-06-08T15:45:44Z A Milnor-Moore theorem for dendriform Hopf 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 purpose of this Note is to announce a Milnor-Moore style theorem for these algebras. 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 envelopping algebra of its brace algebra of primitive elements. One of the ingredients of the proof is the construction of Eulerian idempotents in this context. © 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. 2001 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07644442_v332_n2_p109_Ronco http://hdl.handle.net/20.500.12110/paper_07644442_v332_n2_p109_Ronco
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description 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 purpose of this Note is to announce a Milnor-Moore style theorem for these algebras. 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 envelopping algebra of its brace algebra of primitive elements. One of the ingredients of the proof is the construction of Eulerian idempotents in this context. © 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.
title A Milnor-Moore theorem for dendriform Hopf algebras
spellingShingle A Milnor-Moore theorem for dendriform Hopf algebras
title_short A Milnor-Moore theorem for dendriform Hopf algebras
title_full A Milnor-Moore theorem for dendriform Hopf algebras
title_fullStr A Milnor-Moore theorem for dendriform Hopf algebras
title_full_unstemmed A Milnor-Moore theorem for dendriform Hopf algebras
title_sort milnor-moore theorem for dendriform hopf algebras
publishDate 2001
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07644442_v332_n2_p109_Ronco
http://hdl.handle.net/20.500.12110/paper_07644442_v332_n2_p109_Ronco
_version_ 1768542893110198272

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