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Bibliography
Ahlfors L.V., Old and new in Möbius groups, Ann. Acad. Sci. Fenn., serie A.1 Math. 9, pp. 93–105, 1984.
Ahlfors L.V., Möbius transformations and Clifford numbers, pp. 65–73 in I. Chavel, M.M. Farkas (eds.), Differential geometry and complex analysis, Springer, Berlin, 1985.
Ahlfors L.V., Möbius transformations in R n expressed through 2 × 2 matrices of Clifford numbers, Complex Variables Theory Appl., 5, pp. 215–224, 1986.
Albert A., Structures of Algebras, American Mathematical Society, vol XXIV, New York, 1939.
Anglès P., Les structures spinorielles conformes réelles, Thesis, Université Paul Sabatier.
Anglès P., Construction de revêtements du groupe conforme d’un espace vectoriel muni d’une métrique de type (p,q), Annales de l’I.H.P., section A, vol XXXIII no 1, pp. 33–51, 1980.
Anglès P., Géométrie spinorielle conforme orthogonale triviale et groupes de spinorialité conformes, Report HTKK Mat A 195, pp. 1–36, Helsinki University of Technology, 1982.
Anglès P., Construction de revêtements du groupe symplectique réel C Sp(2r R) Géométrie conforme symplectique réelle. Définition des structures spinorielles conformes symplectiques réelles, Simon Stevin (Gand-Belgique), vol 60 no 1, pp. 57–82, Mars 1986.
Anglès P., Algèbres de Clifford C r,s des espaces quadratiques pseudo-euclidiens standards E r,s et structures correspondantes sur les espaces de spineurs associés. Plongements naturels de quadriques projectives Q(E r,s) associés aux espaces E r,s. Nato ASI Séries vol 183, 79–91, Clifford algebras édité par JSR Chisholm et A.K. Common D. Reidel Publishing Company, 1986.
Anglès P., Real conformal spin structures on manifolds, Scientiarum Mathematicarum Hungarica, vol 23, pp., Budapest, Hungary, 1988.
Anglès P. and R. L. Clerc, Operateurs de creation et d’annihilation et algèbres de Clifford, Ann. Fondation Louis de Broglie, vol. 28, no 1, pp. 1–26, 2003.
Artin E., Geometric Algebra, Interscience, 1954; or in French, Algèbre géométrique, Gauthier-Villars, Paris, 1972.
Atiyah M. F., R. Bott and A. Shapiro, Clifford Modules, Topology, vol 3, pp. 3–38, 1964.
Barbance Ch., Thesis, Paris, 1969.
Bateman H., The conformal transformations of a space of four dimensions and their applications to geometrical optics, J. of London Mathematical Society, 8, 70, 1908.
Bateman H., The transformation of the Electrodynamical Equations, J. of London Mathematical Society, 8, 223, 1909.
Benedetti R. and C. Petronio, Lectures on hyperbolic geometry, Springer, pp. 7–22, 1992.
Berg M., DeWitt-Morette C., Gwo S. and Kramer E., The Pin groups in physics: C, P and T, Rev. Math. Phys., 13, 2001.
Berger M., Géométrie Différentielle, Armand Colin, Paris, 1972.
Berger M., Géométrie, vol. 1–5, Cedic Nathan, Paris, 1977.
Bourbaki N., Algèbre—Chapitre 9: Formes sesquilineaires et quadratiques, Hermann, Paris, 1959.
Bourbaki N., Elements d’histoire des Mathématiques, Hermann, Paris, p. 173, 1969.
Brauer R. andWeyl H., American J. of Math., pp. 57–425, 1935.
Cartan E., Annales de l’ E.N.S., 31, pp. 263–355, 1914.
Cartan E., La déformation des hypersurfaces dans l’espace conforme réel à ν gε g dimensions, Bull. Soc. Math. France, 45, pp. 57–121, 1917.
Cartan E., Les espaces à connexions conformes, Annales de la Société polonaise de Maths., 2, pp. 171–221, 1923.
Cartan E., Les groupes projectifs qui ne laissent invariante aucune multiplicité plane, Bull. Soc. Math. de France, 41, pp. 1–53, 1931.
Cartan E., Leçons sur la théorie des spineurs, Hermann, Paris, 1938.
Cartan E., The theory of Spinors, Hermann, Paris, 1966.
Chevalley C., Theory of Lie groups, Princeton University Press, 1946.
Chevalley C., The Algebraic theory of Spinors, Columbia University Press, NewYork, 1954.
Cnops J., Vahlen matrices for non-definite matrices, pp. 155–164 in R. Ablamowicz, P. Lounesto, J. M. Parra (eds.), Clifford algebras with numery and symbolic computations, Birkhäuser, Boston, MA, 1996.
Constantinescu-Cornea, Ideale Ränder Riemannscher Flächen, Springer-Verlag, Berlin, 1963.
Crumeyrolle A., Structures spinorielles, Ann. I.H.P., Sect. A, vol. XI, no 1, pp. 19–55, 1964.
Crumeyrolle A., Groupes de spinorialité, Ann. I.H.P., Sect. A, vol. XIV, no 4, pp. 309–323, 1971.
Crumeyrolle A., Dérivations, formes, opérateurs usuels sur les champs spinoriels, Ann. I.H.P., Sect. A, vol. XVI, no 3, pp. 171–202, 1972.
Crumeyrolle A., Algèbres de Clifford et spineurs, Université Toulouse III, 1974.
Crumeyrolle A., Fibrations spinorielles et twisteurs généralisés, Periodica Math. Hungarica, vol. 6-2, pp. 143–171, 1975.
Crumeyrolle A., Algèbres de Clifford dégénérées et revêtements des groupes conformes affines orthogonaux et symplectiques, Ann. I.H.P., Sect. A, vol. XXIII, no 3, pp. 235–249, 1980.
Crumeyrolle A., Bilinéarité et géométrie affine attachées aux espaces de spineurs complexes Minkowskiens ou autres, Ann. I.H.P., Sect. A, vol. XXXIV, no 3, pp. 351–371, 1981.
Cunningham E., The principle of relativity in Electrodynamics and an extension Thereof, J. of London Mathematical Society, 8, 77, 1909.
D’Auria R., Ferrara S., Lledó MA., Varadarajan VS., Spinor algebras, J. Geom. Phys., 40, pp. 101–128, 2001.
Deheuvels R., Formes Quadratiques et groupes classiques, Presses Universitaires de France, Paris, 1981.
Deheuvels R., Groupes conformes et algèbres de Clifford, Rend. Sem. Mat. Univers. Politech. Torino, vol. 43, 2, pp. 205–226, 1985.
Dieudonné J., Les determinants sur un corps non commutatif, Bull. Soc. Math. de France, 71, pp. 27–45, 1943.
Dieudonné J., On the automorphisms of the classical groups, Memoirs of Am. Math. Soc., n° 2, pp. 1–95, 1951.
Dieudonné J., On the structure of Unitary groups, Trans. Am. Math. Soc., 72, 1952.
Dieudonné J., La géométrie des groupes classiques, Springer-Verlag, Berlin, Heidelberg, New York, 1971.
Dieudonné J., Eléments d’analyse, Tome 4, Gauthier-Villars, 1971.
Dieudonné J., Sur les groupes classiques, Hermann, Paris, 1973.
Dirac P. A. M., Annals Mathematics, pp. 37–429, 1936.
Ehresmann C., Les connections infinitésimales dans un espace fibré différentiable, Colloque de Topologie, Brussels, pp. 29–55, 1950.
Elstrodt J., Grunewald F. and Mennicke J., Vahlen’s groups of Clifford matrices and spin groups, Math. Z., 196, pp. 369–390, 1987.
Ferrand J., Les géodésiques des structures conformes, CRAS Paris, t. 294, May 17 1982.
FialkowA., The conformal theory of curves, Ann. Math. Soc.Trans., 51, pp. 435–501, 1942.
Fillmore J.P. and A. Springer, Möbius groups over general fields using Clifford algebras associated with spheres, Int. J. Theor. Phys., 29, pp. 225–246, 1990.
Gilbert J. and M. Murray, Clifford algebras and Dirac operators in harmonic analysis, Cambridge Studies in Advanced Mathematics, Cambridge University Press, pp. 34–38 and pp. 278–296, 1991.
Greub, Halperin, Vanstone, Connections, curvature and cohomology, vol. 1, Academic Press, 1972.
Greub, Halperin, Vanstone, Connections, curvature and cohomology, vol. 2, Academic Press, 1972.
Greub W. and Petry R., On the lifting of structure groups, Lecture notes in mathematics, no 676. Differential geometrical methods in mathematical physics, Proceedings, Bonn, pp. 217–246, 1977.
Haantjes J., Conformal representations of an n-dimensional Euclidean space with a non-definitive fundamental form on itself, Nedel. Akad. Wetensch. Proc. 40, pp. 700–705, 1937.
Helgason S., Differential Geometry and Symmetric Spaces, Academic Press, New York and London, 1962.
Hepner W.A., The inhomogeneous linear group and the conformal group, Il Nuevo Cimento, vol. 26, pp. 351–368, 1962.
Hermann R., Gauge fields and Cartan–Ehresmann connections, Part A, Math. Sci. Press, Brookline, 1975.
Hestenes D. and G. Sobczyk, Clifford algebras to geometric calculus, Reidel, Dordrecht, 1984, 1987.
Husemoller D., Fiber bundles, McGraw Inc., 1966.
Jadczyk A. Z., Some comments on conformal connections, Preprint no 443, I.F.T. UniwersytetuWroclawskiego, Wroclaw, November 1978. Proceedings Differential Geometrical Methods in Maths. Physics, Springer, LNM 836, 202–210, 1979.
Kahan T., Théorie des groupes en physique classique et quantique, Tome 1, Dunod, Paris, 1960.
Karoubi M., Algèbres de Clifford et K-théorie, Annales Scientifiques de l’E.N.S., 4° série, tome 1, pp. 14-270, 1968.
Kobayashi S. and Nomizu K., Foundations of differential geometry, vol. 1, Interscience Publishers, New York, 1963.
Kobayashi S., Transformation groups in differential geometry, Springer-Verlag, Berlin, 1972.
Kosmann-Schwarzbach Y., Dérivée de Lie des spineurs, Thesis, Paris, 1969; Annali di Mat. Pura Applicata, IV, vol. 91, pp. 317–395, 1972.
Kosmann-Schwarzbach Y., Sur la notion de covariance en relativité générale, Journées relativistes de Dijon, 1975.
Kuiper N.H., On conformally flat spaces in the large, Ann. of Math., vol. 50, no 4, pp. 916–924, 1949.
Lam T.Y., The algebraic theory of quadratic forms,W.A. Benjamin Inc., 1973.
Lichnerowicz A., Eléments de calcul tensoriel, A. Colin, Paris, 1950.
Lichnerowicz A., Théories relativistes de la gravitation et de l’électromagnétisme, Masson.
LichnerowiczA., Champs spinoriels et propagateurs en relativité générale, Bull. Soc. Math. France, 92, pp. 11–100, 1964.
Lichnerowicz A., Champ de Dirac, champ du neutrino et transformations C. P. T. surun espace-temps courbe, Ann. Inst. H. Poincaré 6 Sect. A.N.S., 1, pp. 233–290, 1964.
Lichnerowicz A., Cours du Collège de France, ronéotypé non publié, 1963–1964.
Lounesto P., Spinor valued regular functions in hypercomplex analysis, Thesis, Report HTKK-Math-A 154, Helsinki University of Technology, 1–79, 1979.
Lounesto P., Latvamaa E., Conformal transformations and Clifford algebras, Proc. Amer. Math. Soc., 79, pp. 533–538, 1980.
Lounesto P. and A. Springer, Möbius transformations and Clifford algebras of Euclidean and anti-Euclidean spaces, in Deformations of Mathematical Structures, J. Lawrynowicz, ed., Kluwer Academic, Dordrecht, pp. 79–90, 1989.
Lounesto P., Clifford algebras and spinors, second edition, Cambridge University Press, London Mathematical Society, Lectures Notes Series, 286, 2001.
Maia M.D., Isospinors, Journal of Math. Physics, vol. 14, no 7, pp. 882–887, 1973.
Maia M.D., Conformal spinors in general relativity, Journal of Math. Physics, vol. 15, no. 4, pp. 420–425, 1974.
Maks J. G., Modulo (1,1) periodicity of Clifford algebras and the generalized (anti-)Möbius transformations, Thesis, Technische Universiteit, Delft, 1989.
Maass H., Automorphe Funktionen von mehreren Veränderlichen und Dirichletsche Reihen, Abh. Math. Sem. Univ. Hamburg, 16, pp. 72–100, 1949.
Milhorat J. L., Sur les connections conformes, Thesis, Université Paul Sabatier, Toulouse, 1985.
Milnor J., Spin structure on manifolds, Enseignement mathématique, Genève, 2 série 9, pp. 198–203, 1963.
Murai Y., On the group of transformations of six dim. spaces, Prog. of Th. Physics, vol. 9, pp. 147–168, 1953.
Murai Y., Conformal groups in Physics, Prog. of Th. Physics, vol. 11, no 45, pp. 441–448, 1954.
Ogiue K., Theory of conformal connections, Kodai Math. Sem. Rep., 19, pp. 193–224, 1967.
O’Meara O.T., Introduction to quadratic forms, Springer-Verlag, Berlin, Göttingen, Heidelberg, 1973.
Penrose R., Twistor algebra, J. of Math. Physics, t. 8, pp. 345–366, 1967.
Penrose R., Twistor quantization and curved space-time, Int. J. of Th. Physics, (I), 1968.
Pham Mau Quan, Introduction à la géométrie des variétés différentiables, Dunod, Paris, 1969.
Popovici I. and D. C. Radulescu, Characterizing the conformality in a Minkowski space, Annales de l’I.H.P., section A, vol. XXXV, no 1, pp. 131–148, 1981.
Porteous I.R., Topological geometry, 2ν δ gdition, Cambridge University Press, 1981.
Postnikov M., Leçons de géométries: Groupes et algèbres de Lie, Trad. Française, Ed. Mir, Moscou, 1985.
Riescz M., Clifford numbers and spinors, Lectures series no 38, University of Maryland, 1958.
Ryan J., Conformal Clifford manifolds arising in Clifford analysis, Proc. R. Irish Acad., Section 1.85, pp. 1–23, 1985.
Ryan J., Clifford matrices, Cauchy–Kowalewski extension and analytic functionals, Proc. Centre Math. Annal Aust. Natl. Univ., 16, pp. 286–299, 1988.
Satake I., Algebraic structures of symmetric domains, Iwanami Shoten publishers and Princeton University Press, 1981.
Schouten J. A. and D. J. Struik, Einführung in die nueren Methoden der Differential- Geometrie, Groningen, Noordhoff, vol. 2, p. 209, 1938.
Segal I., Positive energy particle models with mass splitting, Proced. of the Nat. Ac. Sc. of U.S.A., Vol. 57, pp. 194–197, 1967.
Serre J.P., Applications algébriques de la cohomologie des groupes, II. Théorie des algèbres simples, Séminaire H. Cartan, E.N.S., 2 exposés 6.01, 6.09, 7.01, 7.11, 1950–1951.
Steenrod N., The topology of fiber bundles, Princeton University Press, New Jersey, 1951.
Sternberg S., Lectures on differential geometry, P. Hall, New-York, 1965.
Sudbery A., Division algebras, pseudo-orthogonal groups and spinors, J. Phys. A. Math. Gen. 17, pp. 939–955, 1984.
Tanaka N., Conformal connections and conformal transformations, Trans. A.M.S., 92, pp. 168–190, 1959.
Toure A., Divers aspects des connections conformes, Thesis, Université Paris VI, 1981.
Vahlen K.-Th., Über Bewegungen und complexen Zahlen, Math. Ann., 55, pp. 585– 593, 1902.
Van der Waerden B.L., Nachr. Ges.Wiss., Göttingen, 100, I, 1929.
Wall C.T.C., Graded algebras anti-involutions, simple groups and symmetric spaces, Bull. Am. Math. Soc., 74, pp. 198–202, 1968.
Weil A., Algebras with involutions and the classical groups, Collected papers, vol. II, pp. 413–447, 1951–1964; reprinted by permission of the editors of Journal of Ind. Math. Soc., Springer-Verlag, New York, 1980.
Wolf J. A., Spaces of constant curvature, Publish or Perish. Inc. Boston, 1974.
Wybourne B.G., Classical groups for Physicists, JohnWiley and sons, Inc. NewYork, 1974.
Yano K., Sur les circonferences généralisées dans les espaces à connexion conforme, Proc. Imp. Acad. Tokyo, 14, pp. 329–332, 1938.
Yano K., Sur la théorie des espaces à connexion conformes, Journal of Faculty of Sciences, Imperial University of Tokyo, vol. 4, pp. 40–57, 1939.
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Anglè, P. (2008). Real Conformal Spin Structures. In: Anglès, P. (eds) Conformal Groups in Geometry and Spin Structures. Progress in Mathematical Physics, vol 50. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4643-1_2
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