Nous étudions en détail le foncteur oubli de la catégorie des
The purpose of this paper is two fold: we study the behaviour of the forgetful functor from
Let
Mots-clés :
@article{AMBP_2010__17_1_47_0, author = {Livernet, Muriel}, title = {From left modules to algebras over an operad: application to combinatorial {Hopf} algebras}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {47--96}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {17}, number = {1}, year = {2010}, doi = {10.5802/ambp.278}, zbl = {1206.18010}, mrnumber = {2674654}, language = {en}, url = {https://www.numdam.org/articles/10.5802/ambp.278/} }
TY - JOUR AU - Livernet, Muriel TI - From left modules to algebras over an operad: application to combinatorial Hopf algebras JO - Annales mathématiques Blaise Pascal PY - 2010 SP - 47 EP - 96 VL - 17 IS - 1 PB - Annales mathématiques Blaise Pascal UR - https://www.numdam.org/articles/10.5802/ambp.278/ DO - 10.5802/ambp.278 LA - en ID - AMBP_2010__17_1_47_0 ER -
%0 Journal Article %A Livernet, Muriel %T From left modules to algebras over an operad: application to combinatorial Hopf algebras %J Annales mathématiques Blaise Pascal %D 2010 %P 47-96 %V 17 %N 1 %I Annales mathématiques Blaise Pascal %U https://www.numdam.org/articles/10.5802/ambp.278/ %R 10.5802/ambp.278 %G en %F AMBP_2010__17_1_47_0
Livernet, Muriel. From left modules to algebras over an operad: application to combinatorial Hopf algebras. Annales mathématiques Blaise Pascal, Tome 17 (2010) no. 1, pp. 47-96. doi : 10.5802/ambp.278. https://www.numdam.org/articles/10.5802/ambp.278/
[1] Structure of the Malvenuto-Reutenauer Hopf algebra of permutations, Adv. Math., Volume 191 (2005) no. 2, pp. 225-275 | DOI | MR | Zbl
[2] Structure of the Loday-Ronco Hopf algebra of trees, J. Algebra, Volume 295 (2006) no. 2, pp. 473-511 | MR | Zbl
[3] Twisted Lie algebras, Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977), II (Lecture Notes in Math.), Volume 658, Springer, Berlin, 1978, pp. 9-15 | MR | Zbl
[4] The Hopf algebras of symmetric functions and quasi-symmetric functions in non-commutative variables are free and co-free, J. Algebra Appl., Volume 8 (2009) no. 4, pp. 581-600 | DOI | MR
[5] Algèbres de Hopf des permutohèdres, associahèdres et hypercubes, Adv. Math., Volume 150 (2000) no. 2, pp. 264-275 | DOI | MR | Zbl
[6] Bigèbres différentielles graduées associées aux permutoèdres, associaèdres et hypercubes, Ann. Inst. Fourier (Grenoble), Volume 50 (2000) no. 4, pp. 1127-1153 | DOI | Numdam | MR | Zbl
[7] Construction de certaines opérades et bigèbres associées aux polytopes de Stasheff et hypercubes, Trans. Amer. Math. Soc., Volume 354 (2002) no. 1, p. 63-74 (electronic) | DOI | MR | Zbl
[8] Opérades différentielles graduées sur les simplexes et les permutoèdres, Bull. Soc. Math. France, Volume 130 (2002) no. 2, pp. 233-251 | Numdam | MR | Zbl
[9] Noncommutative symmetric functions VI: free quasi-symmetric functions and related algebras, Internat. J. Algebra Comput., Volume 12 (2002) no. 5, pp. 671-717 | DOI | MR | Zbl
[10] Bidendriform bialgebras, trees, and free quasi-symmetric functions, J. Pure Appl. Algebra, Volume 209 (2007) no. 2, pp. 439-459 | DOI | MR | Zbl
[11] Koszul duality of operads and homology of partition posets, Homotopy theory: relations with algebraic geometry, group cohomology, and algebraic
[12] Lie theory for Hopf operads, J. Algebra, Volume 319 (2008), pp. 4899-4920 | DOI | MR | Zbl
[13] Scindement d’associativité et algèbres de Hopf, Actes des Journées Mathématiques à la Mémoire de Jean Leray (Sémin. Congr.), Volume 9, Soc. Math. France, Paris, 2004, pp. 155-172 | MR
[14] On the algebra of quasi-shuffles, Manuscripta Math., Volume 123 (2007) no. 1, pp. 79-93 | DOI | MR | Zbl
[15] Hopf algebra of the planar binary trees, Adv. Math., Volume 139 (1998) no. 2, pp. 293-309 | DOI | MR | Zbl
[16] Trialgebras and families of polytopes, Homotopy theory: relations with algebraic geometry, group cohomology, and algebraic
[17] On the structure of cofree Hopf algebras, J. reine angew. Math., Volume 592 (2006), pp. 123-155 | DOI | MR | Zbl
[18] Duality between quasi-symmetric functions and the Solomon descent algebra, J. Algebra, Volume 177 (1995) no. 3, pp. 967-982 | DOI | MR | Zbl
[19] Construction de trigèbres dendriformes, C. R. Math. Acad. Sci. Paris, Volume 342 (2006) no. 6, pp. 365-369 | MR | Zbl
[20] Weak Bruhat order on the set of faces of the permutohedron and the associahedron, J. Algebra, Volume 299 (2006) no. 2, pp. 648-678 | DOI | MR | Zbl
[21] On descent algebras and twisted bialgebras, Mosc. Math. J., Volume 4 (2004) no. 1, p. 199-216, 311 | MR | Zbl
[22] Trees, set compositions and the twisted descent algebra, J. Algebraic Combin., Volume 28 (2008) no. 1, pp. 3-23 | DOI | MR | Zbl
[23] Algèbres de Hopf de tableaux, Ann. Sci. Math. Québec, Volume 19 (1995) no. 1, pp. 79-90 | MR | Zbl
[24] The equivalence of certain categories of twisted Lie and Hopf algebras over a commutative ring, J. Pure Appl. Algebra, Volume 86 (1993) no. 3, pp. 289-326 | DOI | MR | Zbl
[25] Relating the associahedron and the permutohedron, Operads: Proceedings of Renaissance Conferences (Hartford, CT/Luminy, 1995) (Contemp. Math.), Volume 202, Amer. Math. Soc., Providence, RI (1997), pp. 33-36 | MR | Zbl
Cité par Sources :