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de

Loïc Foissy


Présentation

CV

Publications

Communications

Enseignement


Thèse de doctorat :

  • Les algèbres de Hopf des arbres enracinés décorées. Pdf.


Habilitation à diriger des recherches :

  • Algèbres de Hopf combinatoires. Pdf.


Publications :

  • A pre-Lie algebra associated to a linear endomorphism and related algebraic structures. Eur. J. Math. 1, no. 1, 78121 (2015). Pdf, arXiv.

  • The Hopf algebra of Fliess operators and its dual pre-Lie algebra. Comm. Algebra 43, no. 10, 45284552 (2015). Pdf, arXiv.

  • The Hopf algebra of finite topologies and T-partitions, en collaboration avec Claudia Malvenuto. J. Algebra 438, 130169.Pdf, arXiv.

  • B_infinity-algebras, their enveloping algebras and finite spaces, en collaboration avec Claudia Malvenuto et Frédéric Patras. To be published in Journal of Pure and Applied Algebra. Pdf, arXiv.

  • A combinatorial non-commutative Hopf algebra of graphs, en collaboration avec Gérard Duchamp, Nguyen Hoang-Nghia, Dominique Manchon et Adrian Tanasa. Discrete Math. Theor. Comput. Sci. 16, no. 1, 355-370 (2014). Pdf, arXiv.

  • Bruhat order on plane posets and applications. J. Combin. Theory Ser. A. 126, 1-23 (2014). Pdf, arXiv.

  • Deformation of the Hopf algebra of plane posets. European J. Combin. 38, 36-40 (2014). Pdf, arXiv.

  • Natural endomorphisms of shuffle algebras, en collaboration avec Frédéric Patras. Int. J. Algebra and Computation 23, no. 4 (2013) 9891009. Pdf, arXiv.

  • Pre-Lie algebras and systems of Dyson-Schwinger equations, Proceedings of the DSFdB2011 Meeting, Strasbourg. Pdf.

  • Ordered forests, permutations and iterated integrals, en collaboration avec Jérémie Unterberger. Int. Math. Res. Notices, no. 4, 846-885 (2013).Pdf, arXiv.

  • Plane posets, special posets and permutations. Adv.Math. 240, 24-60 (2013). Pdf, arXiv.

  • Algebraic structures on double and plane posets. Journal of Algebraic Combinatorics 37 (2013), no. 1, 39-66. Pdf, arXiv, MathSciNet.

  • Ordered forests and parking functions. International Mathematics Research Notices 7, 1603-1633 (2012). Pdf, arXiv, MathSciNet.

  • Free and cofree Hopf algebras. J. Pure App. Algebra 216 (2012), no. 2, 480-494. Pdf, arXiv, MathSciNet.

  • Polynomial realization of some combinatorial Hopf algebras, en collaboration avec Jean-Christophe Novelli et Jean-Yves Thibon. Journal of Noncommutative Geometry (2012). Pdf, arXiv.

  • Primitive elements of the Hopf algebra of free quasi-symmetric functions. Combinatorics and Physics, Contemp. Math. 539 (2011), 79-88. Pdf, MathSciNet.

  • Lie algebra associated to systems of Dyson-Schwinger equations. Adv. Math.226 (2011), no. 6, 4702-4730. Pdf, arXiv, MathSciNet.

  • Hopf subalgebras of the Hopf algebra of rooted trees coming from Dyson-Schwinger equations and Faà di Bruno Lie algebras. Motives, QFT and PsDO, Clay Math. Proc. 12 (2010), 189-210. Pdf, notebook MuPAD, MathSciNet.

  • Classification of systems of Dyson-Schwinger equations in the Hopf algebra of decorated rooted trees. Adv. Math. 224 (2010), 2094-2150. Pdf, arXiv, MathSciNet.

  • The infinitesimal Hopf algebra and the operads of planar forests. International Mathematics Research Notices (2009), no. 3, 395-435. Pdf, arXiv, MathSciNet.

  • Free brace algebras are free prelie algebras. Comm. Algebra 38 (2010), no. 9, 3358-3369. Pdf, arXiv, MathSciNet.

  • The infinitesimal Hopf algebra and the poset of planar forests. Journal of Algebraic Combinatorics 30 (2009), 277-309. Pdf, arXiv MathSciNet.

  • Faà di Bruno subalgebras of the Hopf algebra of planar trees from combinatorial Dyson-Schwinger equations. Adv. Math. 218 (2008), 136-162. Pdf, arXiv, MathSciNet.

  • Le groupe des traces de Poisson de la variété quotient h+h^*/W en rang 2, en collaboration avec Jacques Alev. Comm. Algebra 37 (2009), no. 1, 368-388. Pdf, arXiv, MathSciNet.

  • Étude de l'algèbre de Lie double des arbres enracinés décorés. Adv.Math. 208 (2007), no.2, 877-904. Pdf, MathSciNet.

  • Bidendriform bialgebras, trees, and free quasi-symmetric functions. J.Pure Appl. Algebra 209 (2007), no. 2, 439-459. Pdf, arXiv, MathSciNet.

  • Quantifications des algèbres de Hopf d'arbres plans décorés et lien avec les groupes quantiques. Bull. Sci. Math. 127 (2003), no. 6, 505-548. Pdf, MathSciNet.

  • Finite-dimensional comodules over the Hopf algebra of rooted trees. J. Algebra 255 (2002), no. 1, 89-120. Pdf, arXiv, MathSciNet.

  • Les algèbres de Hopf des arbres enracinés décorés. II. Bull. Sci. Math. 126 (2002), no. 4, 249-288. Pdf, arXiv, MathSciNet.

  • Les algèbres de Hopf des arbres enracinés décorés. I. Bull. Sci. Math. 126 (2002), no. 3, 193-239. Pdf, arXiv, MathSciNet.


Preprints :

  • Multigraded Dyson-Schwinger systems. Pdf, arXiv.

  • A divisibility result on combinatorics of generalized braids, en collaboration avec Jean Fromentin. Pdf, arXiv.

  • Free quadri-algebras and dual quadri-algebras. Pdf, arXiv.

  • The Hopf algebra of finite topologies and mould composition, en collaboration avec Frédéric Fauvet et Dominique Manchon. Pdf, arXiv.

  • Examples of Com-PreLie Hopf algebras. Pdf, arXiv.

  • Deformations of shuffles and quasi-shuffles, en collaboration avec Frédéric Patras et Jean-Yves Thibon. Pdf, arXiv.

  • General Dyson-Schwinger equations and systems. Pdf, arXiv.

  • Left ideals in an enveloping algebra, prelie products and applications to simple complex Lie algebras. Pdf, programmes MuPAD, arXiv.

  • Systems of Dyson-Schwinger equations. Pdf, arXiv.

  • The operads of planar forest are Koszul. Pdf, arXiv.

  • An introduction to Hopf algebras of trees. Pdf.

  • Quantization of the Hopf algebras of planar decorated rooted trees. Pdf.

  • L'algèbre des invariants d'un groupe de Coxeter agissant sur un multiple de sa représentation standard. Pdf, arXiv.