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Abstract:

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.

Registro:

Documento: Artículo
Título:Eulerian idempotents and Milnor-Moore theorem for certain non-cocommutative Hopf algebras
Autor:Ronco, M.
Filiación:Depto. V Ciclo Básico Común., Univ. De Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Palabras clave:Dendriform algebra; Hopf algebra
Año:2002
Volumen:254
Número:1
Página de inicio:152
Página de fin:172
DOI: http://dx.doi.org/10.1016/S0021-8693(02)00097-2
Título revista:Journal of Algebra
Título revista abreviado:J. Algebra
ISSN:00218693
CODEN:JALGA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v254_n1_p152_Ronco

Referencias:

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Citas:

---------- APA ----------
(2002) . Eulerian idempotents and Milnor-Moore theorem for certain non-cocommutative Hopf algebras. Journal of Algebra, 254(1), 152-172.
http://dx.doi.org/10.1016/S0021-8693(02)00097-2
---------- CHICAGO ----------
Ronco, M. "Eulerian idempotents and Milnor-Moore theorem for certain non-cocommutative Hopf algebras" . Journal of Algebra 254, no. 1 (2002) : 152-172.
http://dx.doi.org/10.1016/S0021-8693(02)00097-2
---------- MLA ----------
Ronco, M. "Eulerian idempotents and Milnor-Moore theorem for certain non-cocommutative Hopf algebras" . Journal of Algebra, vol. 254, no. 1, 2002, pp. 152-172.
http://dx.doi.org/10.1016/S0021-8693(02)00097-2
---------- VANCOUVER ----------
Ronco, M. Eulerian idempotents and Milnor-Moore theorem for certain non-cocommutative Hopf algebras. J. Algebra. 2002;254(1):152-172.
http://dx.doi.org/10.1016/S0021-8693(02)00097-2