S. Albeverio and R. Hoegh-krohn, Brownian motion, Markov cosurfaces and Higgs fields; Fundamental aspects of quantum field theory (Corno, 1985), NATO, Adv. Sci. Inst. Ser. B. Phys, vol.144, pp.95-104, 1986.

S. Albeverio, R. Hoegh-krohn, and H. Holden, Markov cosurfaces and gauge fields, Acta Phys. Austr, vol.26, pp.211-231, 1984.

S. Albeverio, R. Hoegh-krohn, and H. Holden, Stochastic multiplicative measures, generalized Markov semi-groups and group-valued stochastic processes and fields, J. Funct. Anal, vol.78, pp.154-184, 1988.

S. Albeverio, R. Hoegh-krohn, and H. Holden, Stochastic Lie group-valued measures and their relations to stochastic curve integrals, gauge fields and Markov cosurfaces, Stochastic processes-mathematical physics, vol.1158, pp.1-24, 1984.

S. Albeverio, R. Hoegh-krohn, and H. Holden, Random fields with values in Lie groups and Higgs fields; in stochastic Processes in Classical and Quantum System Proceedings, Lect. Notes in Physics, vol.262, p.13, 1985.

A. Batubenge and P. Ntumba, On the way to Frölicher Lie groups Quaestionnes mathematicae, vol.28, pp.73-93, 2005.

G. Bogfjellmo and A. Schmeding, The Lie group structure of the Butcher group, Foundations of Computational Mathematics, vol.17, issue.1, p.159, 2017.

G. Bogfjellmo, R. Dahmen, and A. Schmeding, Character groups of Hopf algebras as infinitedimensional Lie groups

, Ann. Inst. Fourier, vol.66, issue.5, pp.2101-2155, 2016.

P. Cartier,

, Groupoïdes de Lie et leurs algebroïdes, Astérisque, vol.987, pp.165-196, 2007.

P. Cherenack and P. Ntumba, Spaces with differentiable structure an application to cosmology Demonstratio Math, vol.34, pp.161-180, 2001.

P. Donato, Revêtements de groupes différentiels Thèse de doctorat d'état, 1984.

A. Frölicher and A. Kriegl, Linear spaces and differentiation theory Wiley series in Pure and Applied Mathematics, 1988.

P. Gilkey, Invariance theory, the heat equation and the Atiyah-Singer index theorem Publish or Perish, 1984.

H. Glöckner, Algebras whose groups of the units are Lie groups Studia Math, vol.153, pp.147-177, 2002.

P. Iglesias and . Diffeology,

A. Kriegl and P. W. Michor, The convenient setting for global analysis Math. surveys and monographs 53, 2000.

M. Laubinger, A Lie algebra for Frölicher groups Indag, Math, vol.21, issue.3, pp.156-174, 2011.

P. Lax, Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure Appl. Math, vol.21, pp.5-405, 1968.

J. Leslie, On a Diffeological Group Realization of certain Generalized symmetrizable Kac-Moody Lie Algebras, J. Lie Theory, vol.13, pp.427-442, 2003.

T. Lévy,

J. Magnot, Structure groups and holonomy in infinite dimensions, vol.128, pp.513-529, 2004.

J. Magnot, Difféologie sur le fibré d'holonomie d'une connexion en dimension infinie, C. R. Math. Acad. Sci. Soc. R. Can, vol.28, pp.4-121, 2006.

J. Magnot, The Schwinger cocycle for algebras with unbounded operators, Bull. Sci. Math, vol.132, issue.2, pp.112-127, 2008.

J. Magnot and . Ambrose, Singer theorem on diffeological bundles and complete integrability of the KP equation, Int. J. Geom. Meth. Mod. Phys, vol.10, issue.9, p.p, 2013.

J. Magnot, The group of diffeomorphisms of a non-compact manifold is not regular Demonstr, Math, vol.51, issue.1, pp.8-16, 2018.

J. Magnot, Remarks on a new discretization scheme for gauge theories, Int. J. Theoret. Phys, vol.57, issue.7, pp.2093-2102, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01807587

J. Magnot, On the differential geometry of numerical schemes and weak solutions of functional equations
URL : https://hal.archives-ouvertes.fr/hal-01961436

J. Magnot and E. G. Reyes, Well-posedness of the Kadomtsev-Petviashvili hierarchy, Mulase factorization, and Frölicher Lie groups
URL : https://hal.archives-ouvertes.fr/hal-02497053

K. Neeb, Towards a Lie theory of locally convex groups, Japanese J. Math, vol.1, pp.291-468, 2006.

H. Omori, Infinite dimensional Lie groups AMS translations of mathematical monographs, p.158, 1997.

A. N. Sengupta, Yang-Mills in two dimensions and Chern-Simons in three, Chern-Simons Theory: 20 years after, pp.311-320, 2011.

J. M. Souriau, Un algorithme générateur de structures quantiques

H. Astérisque and . Série, , pp.341-399, 1985.

T. Robart, Sur l'intégrabilité des sous-algèbres de Lie en dimension infinie; Can, J. Math, vol.49, issue.4, pp.820-839, 1997.

J. Watts, Diffeologies, differentiable spaces and symplectic geometry

U. Larema, Angers, 2 Bd Lavoisier, 49045 Angers cedex 1, France and Lycée Jeanne d