Journal of Mathematical Sciences

, Volume 80, Issue 3, pp 1837–1853 | Cite as

Some models in differential geometry

  • A. M. Nikitin
Article
  • 14 Downloads

Abstract

Some variants of the axiomatics of the algebras of “vector fields” in models of noncommutative differential geometry are considered. In the case of a commutative model (the de Rham complex) a matrix analogue of the Kadomtsev-Petviashvili hierarchy is constructed. The corresponding Sato system is presented. The method of deformations of D-modules is used. Bibliography: 14 titles.

Keywords

Vector Field Differential Geometry Matrix Analogue Noncommutative Differential Geometry Commutative Model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    M. Karoubi, “Homologie cyclique etK-theorie,”Asterisque, No. 149 (1987).Google Scholar
  2. 2.
    M. Dubois-Violette, “Derivations et calcul differential non commutatif,”C. R. Acad. Sci., Paris, Ser. 1. Math.,307, 403–408 (1988).MATHMathSciNetGoogle Scholar
  3. 3.
    A. A. Kirillov,Elements of Representation Theory [in Russian], Moscow (1978).Google Scholar
  4. 4.
    F. W. Kamberm and Ph. Tondeur, “Foliated bundles and characteristic classes,”Lect. Notes Math.,493 (1975).Google Scholar
  5. 5.
    D. Gurevich, A. Radul, and V. Rubtsov, “Noncommutative differential geometry related with the Yang-Baxter equation,”Zap. Nauchn. Semin. POMI,199, 51–70 (1992).Google Scholar
  6. 6.
    J. L. Verdier, “Les représentations des algèbres de Lie affines: applications à quelques problèms de physique (d'après E. Date, M. Jimbo, M. Kashiwara, T. Miwa),”Séminaire Bourbaki, 34-eannée, No. 596, 1–13 (1981/82).Google Scholar
  7. 7.
    G. B. Segal and G. Wilson, “Loop groups and equations of KdV type,”Publ. Math. I.H.E.S.,61, 5–65 (1985).MathSciNetGoogle Scholar
  8. 8.
    T. Shiota, “Characterization of Jacobian varieties in terms of soliton equations,”Invent. Math.,83, 333–382 (1986).CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Y. Ohyama, “Self-duality and integrable systems,”Publ. R. I. M. S.,26, 701–722 (1990).MATHMathSciNetGoogle Scholar
  10. 10.
    Yu. I. Manin and A. O. Radul, “A supersymmetric extension of the Kadomtsev-Petviashvili hierarchy,”Commun. Math. Phys.,98, 65–78 (1985).CrossRefMathSciNetGoogle Scholar
  11. 11.
    K. Ueno and H. Yamada, “Supersymmetric extension of the Kadomtsev-Petviashvili hierarchy and the universal super Grassmann manifold,”Adv. Stud. Pure Math.,16, 373–426 (1988).MathSciNetGoogle Scholar
  12. 12.
    M. Mulase, “A new super KP system and a characterization of the Jacobians of arbitrary algebraic super curves,”J. Diff. Geom.,34, 651–680 (1991).MATHMathSciNetGoogle Scholar
  13. 13.
    M. Sato and Y. Sato, “Soliton equations as dynamical systems on infinite-dimensional Grassmann manifold,”Lect. Notes. Num. Appl. Anal.,5, 259–271 (1982).Google Scholar
  14. 14.
    A. Newell,Solitons in Mathematics and Physics, SIAM (1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • A. M. Nikitin

There are no affiliations available

Personalised recommendations