Page Algèbre de Frédéric Patras

FREDERIC PATRAS

PAGE DEDIEE A L'ALGEBRE, LA COMBINATOIRE ET LA TOPOLOGIE

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THEMES DE RECHERCHE / RESEARCH THEMES

Algèbres de Hopf / Hopf algebras
Combinatoire algébrique / Algebraic combinatorics
Opérades / Operads
Théorie de Lie / Free Lie algebras
Topologie algébrique / Algebraic topology

LIVRE / BOOK

La Pensée mathématique contemporaine. Coll. Science, histoire et société, P.U.F., 2001 (2 ed.: 2002).

Il pensiero matematico contemporaneo. Trad. It. G. de Vivo e P. Pagli, Bollati Boringhieri, Collana Saggi Scienze, 2006.

Classical Hopf Algebras and Their Applications. P. Cartier and F. Patras. Algebra and Applications, volume 29, Springer, 2021.

ARTICLES

With L. Foissy, Commutative B-infinity algebras are shuffle algebras, arXiv:2401.13317.

With Vane Jacky III Batkam Mbatchou and Calvin Tcheka, Posets, their incidence algebras and relative operads, and the cohomology comparison theorem, arXiv:2310.10288.

With R. Chétrite, Algebraic structures underlying quantum independences : Theory and Applications, arXiv:2210.09264.

With Ilya Chevyrev, Kurusch Ebrahimi-Fard, Algebraic groups in non-commutative probability theory revisited. arXiv:2208.02585.

With Kurusch Ebrahimi-Fard, Nikolas Tapia, Lorenzo Zambotti, Shifted substitution in non-commutative multivariate power series with a view toward free probability. SIGMA 19 (2023), 038, 17p.

With Adrian Celestino, A forest formula for pre-Lie exponentials, Magnus' operator and cumulant-cumulant relations. arXiv:2203.1196810.

With Kurusch Ebrahimi-Fard, N. Tapia, L. Zambotti Wick polynomials in non-commutative probability: a group-theoretical approach. Canad J Math, Vol. 74 (6) 2022, 1673-1699.

With Kurusch Ebrahimi-Fard, From iterated integrals and chronological calculus to Hopf and Rota-Baxter algebras. Algebra and Applications 2, Combinatorial algebra and Hopf algebras, ed. A. Makhlouf, ISTE Ltd-Wiley, 2021 55-118.

With K. Ebrahimi-Fard Quasi-shuffle algebras in non-commutative stochastic calculus. In: Ugolini, S., Fuhrman, M., Mastrogiacomo, E., Morando, P., Rüdiger, B. (eds) Geometry and Invariance in Stochastic Dynamics. RTISD19 2019. Springer Proceedings in Mathematics & Statistics, vol 378. Springer (2021), 89-112.

With Patrick Cassam-Chenai, Guillaume Dhont Molien functions and generalized integrity bases for SO(3) and related groups. J. Math Chem (59) 2021 2294-2326.

With Kurusch Ebrahimi-Fard, A group-theoretical approach to conditionally free cumulants. in Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA),F. Chapoton et al. eds, IRMA Lectures in Mathematics and Theoretical Physics Vol.31, (2020), 67-94.

With Kurusch Ebrahimi-Fard, Loic Foissy and Joachim Kock, Operads of (noncrossing) partitions, interacting bialgebras, and moment-cumulant relations. Advances in Mathematics 369 (2020) 107170.

With Loic Foissy, Surjections and double posets. Séminaire Lotharingien de Combinatoire 82 (2020), Article B82a.

With Loic Foissy, Lie theory for quasi-shuffle bialgebras. in Symmetril Moulds, Generic Group Schemes, Resummation of MZVs. In: Burgos Gil J. et al. (eds) Periods in Quantum Field Theory and Arithmetic. ICMAT-MZV 2014. Springer Proceedings in Mathematics and Statistics, vol 314. Springer, Cham (2020) 483-540.

With Claudia Malvenuto, Symmetril moulds, generic group schemes, resummation of MZVs. in Symmetril Moulds, Generic Group Schemes, Resummation of MZVs. In: Burgos Gil J. et al. (eds) Periods in Quantum Field Theory and Arithmetic. ICMAT-MZV 2014. Springer Proceedings in Mathematics and Statistics, vol 314. Springer, Cham (2020) 377-398.

With K. Ebrahimi-Fard, Shuffle group laws. Applications in free probability. Proc. London Math. Soc. Volume 119, Issue 3, September 2019, 814-840.

With K. Ebrahimi-Fard, Monotone, free, and boolean cumulants: a shuffle algebra approach. Advances in Mathematics 328 (2018) 112-132.

With F. Menous, Renormalization: a quasi-shuffle approach. Computation and Combinatorics in Dynamics, Stochastics and Control: The Abel Symposium 2016. Celledoni, E. et al. Springer (2018), pp. 599-628.

With Mahdi J. Hasan Al-Kaabi, Dominique Manchon, Monomial bases and pre-Lie structure for free Lie algebras. Journal of Lie Theory 28 (2018), No. 4, 941-967.

With Frédéric Menous, Right-handed bialgebras and the Prelie forest formula. Annales I.H.P. Série D, Volume 5, Issue 1, 2018, 103-125.

With Loic Foissy and Claudia Malvenuto, A theory of pictures for quasi-posets. J. Algebra, (477), 496-515, 2017..

With Loic Foissy and Claudia Malvenuto, Infinitesimal and B-infinity algebras, finite spaces, and quasi-symmetric functions. J. Pure Appl. Algebra, 220 (6), 2016, 2434-2458.

With K. Ebrahimi-Fard, The splitting process in free probability theory. International Mathematics Research Notices 2015; doi: 10.1093/imrn/rnv209.

With Loïc Foissy and Jean-Yves Thibon, Deformations of shuffles and quasi-shuffles. Annales Inst. Fourier, Tome 66, no 1 (2016), p. 209-237.

With K. Ebrahimi-Fard, Cumulants, free cumulants and half-shuffles. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences Vol. 471, No. 2176, (2015) p. 20140843.

With K. Ebrahimi-Fard, The preLie structure of the time-ordered exponential. Lett. Math. Phys. (2014), 104, 1281–1302.

With K. Ebrahimi-Fard, La structure combinatoire du calcul intégral, Gazette des mathématiciens, 138, Octobre 2013, 5-22. English version

With F. Menous Logarithmic Derivatives and Generalized Dynkin Operators. Journal of Algebraic Combinatorics: Volume 38, Issue 4 (2013), Page 901-913

With J.C. Novelli and J.Y. Thibon. Natural endomorphisms of quasi-shuffle Hopf algebras. Bull. Soc. math. France 141 (1), (2013), p. 107-130

With L. Foissy Natural endomorphisms of shuffle algebras Int. J. Algebra and Computation Vol. 23, No. 4 (2013) 989–1009.

With F. Chapoton Enveloping algebras of preLie algebras, Solomon idempotents and the Magnus formula Int. J. Algebra and Computation Vol. 23, No. 4 (2013) 853–861

With M. Bauer, R. Chetrite and K. Ebrahimi-Fard Time-ordering and a generalized Magnus expansion Letters Math. Phys. (2013), 103 (3), 331-350.

With K. Ebrahimi-Fard Exponential Renormalization II: Bogoliubov's R-operation and momentum subtraction schemes J. Math. Phys. 53, 083505 (2012)

With Ch. Brouder, G. Duchamp and G. Z. Toth. The Rayleigh-Schrödinger perturbation series of quasi-degenerate systems. Int. J. Quantum Chem. Volume 112, Issue 10 (2012) Pages: 2256–2266.

With Ch. Brouder. Nonlocal, noncommutative diagrammatics and the linked cluster Theorems J. Math. Chem. (2012) Volume 50, Number 3, Pages 552-576

With Ch. Brouder. Decomposition into one-particle irreducible Green functions in many-body physics. Combinatorics and Physics Eds Ebrahimi-Fard, Marcolli, van Suijlekom, Contemporary Mathematics Vol. 539, (2011), 1--25.

With K. Ebrahimi-Fard. Exponential renormalization. Annales Henri Poincaré 11 (5), (2010), 943--971.

With Ch. Brouder and A. Mestre. Tree expansions in time-dependent perturbation theory. J. Math. Phys. 51, 072104/1-25 (2010)

With Ch. Brouder. Hyperoctahedral Chen calculus for effective Hamiltonians. J. Algebra 322 (2009), 4105-4120.

Dynkin operators and renormalization group actions in pQFT. in: Vertex Operator Algebras and Related Areas, Eds M. Bergvelt, G. Yamskulna, W. Zhao, Contemp. Math. vol. 497 (2009), 169-184.

A noncommutative Bohnenblust-Spitzer identity for Rota-Baxter algebras solves Bogolioubov's recursion . Journal of Noncommutative Geometry , Vol. 3, Issue 2 (2009), 181-222.

With P. Cassam-Chenai. Symmetry-Adapted Polynomial Basis for Global Potential Energy Surfaces - Applications to XY4 Molecules . J. Math. Chem. 44, 938-966, (2008)

< With K. Ebrahimi-Fard and D. Manchon. New identities in dendriform algebras . J. Algebra 320 (2), 708-727, (2008)

With M. Livernet. Lie theory for Hopf operads . J. Algebra 319 (12), 4899-4920 (2008)

With K. Ebrahimi-Fard. A Zassenhaus-type algorithm solves the Bogoliubov recursion. Bulgarian J. of Physics. Lie Theory and its Applications in Physics VII, 35 (s1), 303-315 (2008)

With M. Schocker. Trees, set compositions and the twisted descent algebra. J. Algebr. Comb, 28, 3-23 (2008)

With K. Ebrahimi-Fard and J. Gracia-Bondia. A Lie theoretic approach to renormalization . Comm. Math. Phys. 276, 519-549 (2007)

With K. Ebrahimi-Fard and J. Gracia-Bondia. Rota-Baxter algebras and new combinatorial identities. Letters in Math. Physics 81, (1), (2007), 61-75.

With P. Solé. The coordinator polynomial of some cyclotomic lattices. European J. Combin. 28, (1), (2007), 17-25.

M. Schocker. Twisted Descent Algebras and the Solomon-Tits Algebra. Adv. in Math. 199 (1) (2006), 151-184.

With C. Reutenauer and M. Schocker. On the Garsia Lie idempotent. Bull. Soc. Math. Canada. (2005), Vol 48, No 3, pp. 445-454.

With C. Reutenauer. On descent algebras and twisted bialgebras. Moscow Math. J. 4 (1), (2004), 199-216.

With P. Cassam-Chenai. Higher order, generalized, Schmidt decompositions for indistinguishable, overlapping particles. Physics Letters A. Vol 326/5-6, (2004), 297-306.

With P. Cassam-Chenai. The Hopf algebra of identical, fermionic particle systems - fundamental concepts and properties. J. Math. Phys. 44, (11), (2003), 4884-4906.

With J.-C. Thomas : Cochain algebras of mapping spaces and finite group actions. Topology and its Applications, 128, (2-3), (2003), 189-207.

Lambda-rings. Handbook of Algebra, Vol. 3. Ed. M. Hazewinkel. Amsterdam: North-Holland. 2003, 961-986.

Brace algebras and the cohomology comparison theorem. ArXiv math.QA/0112177 (2003).

With C. Reutenauer : Lie representations and an algebra containing Solomon's. J. Alg. Comb, 16, (2002), 301-314.

With C. Reutenauer. On Dynkin and Klyachko idempotents in graded bialgebras. Adv. Appl. Math. 28, (3), (2002), 560-579.

Generic algebras and iterated Hochschild homology. J. Pure Appl. Algebra. 162, (2001), 337-357.

Modèles combinatoires et géométriques pour les algèbres de Hopf et l'homologie des algèbres. Thèse d'habilitation à diriger des recherches, Juin 2000, Université de Nice.

Adams operations, algebras up to homotopy and cyclic homology. Topology. 39, (6), (2000), 1089-1101.

With C. Reutenauer. Higher Lie idempotents. J. Algebra 222, (1999), 51-64.

A Leray theorem for the generalization to operads of Hopf algebras with divided powers. J. Algebra 218, (1999), 528-542.

Adams operations and periodic cyclic cohomology. Algebraic K-Theory and its Applications, Proc Symp ICTP, Trieste, World Scientific (Singapore) (1999), 567-588.

L'homologie générique est un foncteur Tor. C. R. Acad. Sci. Paris., t. 328, Série I, (1999), 569-572.

Adams operations, iterated integrals and free loop spaces cohomology. J. Pure Appl. Algebra. 114, (1997), 273-286.

Lambda-anneaux non commutatifs.Comm. in Algebra 23, 6 (1995), 2067-2078.

Le calcul de Schubert des permutations décomposables. Sémin. Lothar. Comb. 35, (1995)

L'algèbre des descentes d'une bigèbre graduée. J. Algebra 170, 2 (1994), 547-566.

La décomposition en poids des algèbres de Hopf. Ann. Inst. Fourier. 43, 4 (1993), 1067-1087.

Homothéties simpliciales. Janvier 1992. Thèse de doctorat. Université Paris 7.

Construction géométrique des idempotents eulériens. Filtration des groupes de polytopes et des groupes d'homologie de Hochschild . Bull. Soc. Math. Fr. 119, (1991), 101-126.

Filtration du groupe des polytopes et lambda-structure du groupe symétrique. C. R. Acad. Sci. Paris. t.310, 1, 7 (1990), 501-504.

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