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

  • Jacqueline F. Rojas Universidade Federal da Paraíba.
  • Ramón Mendoza Universidade Federal de Pernambuco.
Palabras clave: Connection, Covariant derivative, Projective module

Resumen

Biografía del autor

Jacqueline F. Rojas, Universidade Federal da Paraíba.
Departamento de Matemática.
Ramón Mendoza, Universidade Federal de Pernambuco.
CCEN - Departamento de Matemática. 

Citas

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

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

[3] 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.

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

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

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

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

[8] 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.

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

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

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

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

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

[14] 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.

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

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

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

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

[19] 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.

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

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

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

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

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

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

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

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

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

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

[30] SWAN, R. G. (1962) Vector Bundles and Projective Modules. EN: Trans. Amer. Math. Soc. 105 (2). [s.l.: s.n.], 264-277.
Publicado
2017-06-02
Cómo citar
Rojas, J., & Mendoza, R. (2017). A brief note on the existence of connections and covariant derivatives on modules. Proyecciones. Journal of Mathematics, 36(2), 225-244. https://doi.org/10.4067/10.4067/S0716-09172017000200225
Sección
Artículos