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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Detalles Bibliográficos
Publicado: 2002
Materias:
Dendriform algebra
Hopf algebra
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v254_n1_p152_Ronco
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
id paper:paper_00218693_v254_n1_p152_Ronco
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spelling paper:paper_00218693_v254_n1_p152_Ronco2023-06-08T14:42:21Z Eulerian idempotents and Milnor-Moore theorem for certain non-cocommutative Hopf algebras 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. 2002 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v254_n1_p152_Ronco 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
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.
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
publishDate 2002
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v254_n1_p152_Ronco
http://hdl.handle.net/20.500.12110/paper_00218693_v254_n1_p152_Ronco
_version_ 1768545079965777920

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