A brief note on the existence of connections and covariant derivatives on modules

Jacqueline Rojas, Ramón Mendoza

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Palabras clave


Connection ; Covariant derivative ; Projective module

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Referencias


ATIYAH, M. F. (1969) Introduction to Commutative Algebra. Reading, MA: Addison-Wesley.

BORN, M. (1926) On quantum mechanics II. EN: Zs. Phys. 35. [s.l.: s.n.], 557-615.

BRUMATTI, P. (1995) The Module of Derivations of a Stanley-Reisner Ring. EN: Proc. Amer. Math. Soc., 23(5). [s.l.: s.n.], 1309-1318.

CARMO, M. P. DO. (1992) Riemannian Geometry. Boston: Birkhäuser.

CARTAN, E. (1924) Les espaces à connexion conforme. EN: Ann. Soc. Polon. Math., 2. [s.l.: s.n.], 171-221.

CARTAN, E. (1924) Sur les variétés à connexion projective. EN: Bull. Soc. Math. France, 52. [s.l.: s.n.], 205-241.

CARTAN, E. (1956) Homological Algebra. [s.l.]: Princeton University Press.

Christoffel, E. B. (1869) Uber die Transformation der homogenen Differentialausdrücke zweiten Grades. EN: Journal für die reine u. angew. Math. (Crelle) 70. [s.l.: s.n.], 46-70.

CONNES, A. (1985) Non-commutative differential geometry. EN: Inst. Hautes Etudes Sci. Publ. Math. 62. [s.l.: s.n.], 257-360.

CONNES, A. (1994) Non-commutative geometry. [s.l.]: Academic Press.

CUNTZ, J. (1995) Algebra Extensions and Nonsingularity. EN: J. Amer. Math. Soc. 8 (2). [s.l.: s.n.], 251-89.

DIRAC, P. (1926) The fundamental equations of quantum mechanics. EN: Proc. Roy. Soc. A 109. [s.l.: s.n.], 642-653.

EISENBUD, D. (1995) Commutative Algebra with a View Toward Algebraic Geometry. EN: Graduate Texts in Math. 150. New York: Springer.

EHRESMANN, C. (1943) Sur les espaces fibrés associés à une variété différentiable. EN: C. R. Acad. Sc. t. 216. [s.l.: s.n.], 628-630.

EHRESMANN, C. (1950) Les connexions infinitésimales dans un espace fibré diffrentiable. EN: Colloque de Toplogie. Bruxelles: CBRM, 29-55.

ELLIS, J. (20??) A Historical Profile of the Higgs Boson. [s.l.: s.n.]. arXiv:1201.6045.

ERIKSEN, E. (1995) Connections and monodromy on modules. EN: Technical Report. [s.l.]: University of Oslo.

ERIKSEN, E (2000) Graded D-modules over Monomial Curves, Ph. D. thesis. [s.l.]: University of Oslo.

GELFAND, I. M. (1943) On the imbedding of normed rings into the ring of operators on a Hilbert space. EN: Math. Sbornik 12(2). [s.l.: s.n.], 197-217.

GOMES, R. (2009) Conexoes e Curvatura: Uma abordagem algébrica, Dissertacao de mestrado, DM-UFPE. [s.l.: s.n.].

HARTSHORNE, R. (1977) Algebraic Geometry. EN: Graduate Texts in Math. 52. New York: Springer.

HENRIQUE, M. L. (2001) Derivacoes e Campos de Vetores, Dissertacao de mestrado, DM-UFPE. [s.l.: s.n.].

FERREIRA, N. (2010) Conexoes e Transporte Paralelo: Abordagem Computacional, Disserta¸ cao de mestrado, DM-UFPE. [s.l.: s.n.].

KOSZUL, J. L. (1950) Homologie et cohomologie des algebres de Lie. EN: Bull. Soc. Math. France, 78. [s.l.: s.n.], 65-127.

KRÄHMER, U. (2009) Dirac Operators, Lecture 1: Projective Modules and Connections. EN: IPM Tehran 19. [s.l.: s.n.].

LEVI-CIVITA, T. (1901) Méthodes de calcul diffrential absolu et leurs applications. EN: Math. Ann. B. 54. , pp. 125-201, (1901).

NESTRUEV, J. (2003) Smooth manifolds and observables. EN: Graduate Texts in Math. 220. New York: Springer-Verlag.

ROJAS, J. (2013) O Funcional de Yang-Mills, Disserta¸ cao de mestrado, DMUFPE. [s.l.: s.n.].

SILVA, R. B. DA. (2013) Existência de conexoes versus módulos projetivos, Disserta¸ cao de mestrado, DM-UFPB. [s.l.: s.n.].

SWAN, R. G. (1962) Vector Bundles and Projective Modules. EN: Trans. Amer. Math. Soc. 105 (2). [s.l.: s.n.], 264-277.


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