M. Aguiar and J. Loday, Quadri-algebras, Journal of Pure and Applied Algebra, vol.191, issue.3, pp.205-221, 2004.
DOI : 10.1016/j.jpaa.2004.01.002

URL : https://hal.archives-ouvertes.fr/hal-00118621

F. Barra and P. Gaspard, On the level spacing distribution in quantum graphs, Journal of Statistical Physics, vol.101, issue.1/2, pp.283-319, 2000.
DOI : 10.1023/A:1026495012522

F. Barra and P. Gaspard, Transport and dynamics on open quantum graphs, Physical Review E, vol.65, issue.1, pp.16205-016226, 2002.
DOI : 10.1103/PhysRevE.65.016205

. Ph and . Biane, Marches de Bernoulli quantiques Séminaire de Probabilités XXIV, Lecture Notes in Math, pp.329-344, 1990.

D. Bures, An Extension of Kakutani's Theorem on Infinite Product Measures to the Tensor Product of Semifinite w ??? -Algebras, Transactions of the American Mathematical Society, vol.135, pp.199-212, 1969.
DOI : 10.2307/1995012

M. Campanino and D. Petritis, On the physical relevance of random walks: an example of random walks on a randomly oriented lattice. eprint arXiv:math.PR/0201150, to appear in proceeding of " Random walks and geometry
URL : https://hal.archives-ouvertes.fr/hal-00121156

M. Campanino and D. Petritis, Random walks on randomly oriented lattices, preprint 2001. eprint arXiv:math

J. S. Carter and M. Saito, Quandle homology theory and cocycle knot invariants. eprint arXiv:math.GT, 112026.

C. Cibils, A quiver quantum group, Communications in Mathematical Physics, vol.122, issue.3, pp.459-477, 1993.
DOI : 10.1007/BF02096879

C. Cibils and M. Rosso, Hopf quivers, Journal of Algebra, vol.254, issue.2, pp.241-251, 2002.
DOI : 10.1016/S0021-8693(02)00080-7

URL : https://hal.archives-ouvertes.fr/hal-00356587

A. Connes, Noncommutative geometry, 1994.

A. Connes and D. Kreimer, Hopf Algebras, Renormalization and Noncommutative Geometry, Communications in Mathematical Physics, vol.199, issue.1, pp.203-242, 1998.
DOI : 10.1007/s002200050499

URL : http://arxiv.org/abs/hep-th/9808042

J. Cuntz and W. Krieger, A class ofC *-algebras and topological Markov chains, Inventiones Mathematicae, vol.98, issue.3, pp.251-268, 1980.
DOI : 10.1007/BF01390048

P. Dehornoy, Braids and self-distributivity [16] J. Dittmann. Yang-Mills equation and Bures metric. eprint: quant-ph/9806018, Lett. Math. Phys, vol.46, issue.4, pp.281-287, 1998.

A. Ambainis, One-dimensional quantum walks, Proceedings of the thirty-third annual ACM symposium on Theory of computing , STOC '01, pp.37-49
DOI : 10.1145/380752.380757

R. Fenn and C. Rourke, RACKS AND LINKS IN CODIMENSION TWO, Journal of Knot Theory and Its Ramifications, vol.01, issue.04, pp.343-406, 1992.
DOI : 10.1142/S0218216592000203

U. Franz, L??vy processes on quantum groups, Contemp. Math, vol.261, pp.161-179, 2000.
DOI : 10.1090/conm/261/04139

R. A. Horn and C. R. Johnson, Matrix Analysis, 1996.

R. L. Hudson, Deformed calculus and quantisation of coboundary Lie bialgebra

R. L. Hudson, CALCULUS IN ENVELOPING ALGEBRAS, Journal of the London Mathematical Society, vol.65, issue.02, pp.361-380, 2002.
DOI : 10.1112/S0024610701002976

V. F. Jones, Index for subfactors, Inventiones Mathematicae, vol.6, issue.1, pp.1-25, 1983.
DOI : 10.1007/BF01389127

S. A. Joni and G. Rota, Coalgebras and Bialgebras in Combinatorics, Studies in Applied Mathematics, vol.2, issue.3, pp.93-139, 1979.
DOI : 10.1002/sapm197961293

C. Kassel, M. Rosso, and V. Turaev, Quantum groups and knot invariants, Panoramas et Synthèses, vol.5, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00124690

A. Katok and B. Hasselblatt, Introduction to the modern theory of dynamical systems, 1995.
DOI : 10.1017/CBO9780511809187

N. Konno, Quantum random walk in one-dimension, Quantum Inf. Process, vol.5, pp.345-354, 2003.

N. Konno, T. Namiki, and T. Soshi, Symmetricity of distribution for one-dimensional Hadamard walk, The Proceedings of the Second Sendai Workshop on Quantum Probability and Quantum Information, pp.11-22, 2004.

T. Kottos and U. Smilansky, Quantum Chaos on Graphs, Physical Review Letters, vol.79, issue.24, p.4794, 1997.
DOI : 10.1103/PhysRevLett.79.4794

T. Kottos and U. Smilansky, Periodic Orbit Theory and Spectral Statistics for Quantum Graphs, Annals of Physics, vol.274, issue.1, p.76, 1999.
DOI : 10.1006/aphy.1999.5904

D. Kreimer, Chen???s iterated integral represents the operator product expansion, Advances in Theoretical and Mathematical Physics, vol.3, issue.3, pp.627-670, 1999.
DOI : 10.4310/ATMP.1999.v3.n3.a7

A. Kumjian, D. Pask, and I. Raeburn, Cuntz???Krieger algebras of directed graphs, Pacific Journal of Mathematics, vol.184, issue.1, pp.161-174, 1998.
DOI : 10.2140/pjm.1998.184.161

. Ph and . Leroux, Ennea-algebras. eprint, arXiv:math.QA/0309213

. Ph and . Leroux, From entangled codipterous coalgebras to coassociative manifolds. eprint arXiv:math.QA, 301080.

. Ph and . Leroux, On representations of braid groups determined by directed graphs. eprint arXiv:math.QA, 210260.

. Ph and . Leroux, Periodic orbits, coassociative grammar and quantum random walk over Z. eprint arXiv:quant-ph, 209100.

. Ph and . Leroux, An algebraic framework of weighted directed graphs, Int. J. Math. Math. Sci, vol.58, 2003.

. Ph and . Leroux, Tiling the (n 2 , 1)-De-Bruijn graph with n coassociative coalgebras, Commun. in Alg, vol.32, issue.8, pp.2949-2967, 2004.

J. Loday, Cyclic homology, 1992.
URL : https://hal.archives-ouvertes.fr/hal-01267296

J. Loday, Une version non commutative des algèbres de Lie: Les algèbres de Leibniz, Enseignement Math, vol.39, pp.269-293, 1993.

J. Loday, Dialgebras. in Dialgebras and related operads, Lecture Notes in Math, pp.7-66, 2001.
DOI : 10.1007/3-540-45328-8_2

URL : https://hal.archives-ouvertes.fr/hal-00139440

J. Loday, Scindement d'associativité et algèbres de Hopf Actes des journées mathématiquesmathématiques`mathématiquesà la mémoire de Jean Leray, Séminaire et Congrès (SMF), pp.155-172, 2002.

J. Loday and M. Ronco, Alg??bres de Hopf colibres, Comptes Rendus Mathematique, vol.337, issue.3, pp.153-158, 2003.
DOI : 10.1016/S1631-073X(03)00288-7

J. Loday and M. Ronco, Trialgebras and families of polytopes, Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic K-theory' Contemporary Mathematics, 2004.
DOI : 10.1090/conm/346/06296

URL : https://hal.archives-ouvertes.fr/hal-00139417

S. Majid, Quantum groups, 1995.

P. Pakonski, K. Zyczkowski, and M. Kus, Classical 1D maps, quantum graphs and ensembles of unitary matrices. eprint arXiv:quant-ph/0011050, J. Phys. A, issue.43, pp.349303-9317, 2001.

T. Pirashvili, Sets with two associative operations, Central European Journal of Mathematics, vol.1, issue.2, pp.169-183, 2003.
DOI : 10.2478/BF02476006

K. H. Rosen, J. G. Michaels, J. L. Gross, J. W. Grossman, and D. R. Shier, Handbook of Discrete and Combinatorial Mathematics [55] Y.A. Rylov. Geometry without topology as a new conception of geometry, Int. J. Math. Math. Sci, issue.12, pp.30733-760, 2000.

W. F. Stinespring, Positive functions on C * -algebras, Proc.Amer, pp.211-216, 1955.

G. Tanner, Spectral statistics for unitary transfer matrices of binary graphs, Journal of Physics A: Mathematical and General, vol.33, issue.18, pp.3567-3585, 2000.
DOI : 10.1088/0305-4470/33/18/304

M. A. Nielsen, Quantum information theory, 1998.
DOI : 10.1017/CBO9780511976667.016

D. Quillen, Superconnections and the Chern character, Topology, vol.24, issue.2, pp.89-95, 1985.
DOI : 10.1016/0040-9383(85)90028-X

D. Quillen, Algebra cochains and cyclic cohomology, Publications math??matiques de l'IH??S, vol.38, issue.2, pp.139-174, 1988.
DOI : 10.1007/BF02698546

M. Schurmann, White noise on bialgebras, Lecture Notes in Math, vol.1544, 1993.
DOI : 10.1007/BFb0089237

E. P. Wigner and M. M. Yanase, On the positive semidefinite nature of a certain matrix expression, Journal canadien de math??matiques, vol.16, issue.0, pp.397-406, 1964.
DOI : 10.4153/CJM-1964-041-x