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Classical superspaces and related structures

  • 4. Superalgebras and Supermanifolds
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Differential Geometric Methods in Theoretical Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 375))

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References

  1. Arnold V., Mathematical methods of classical mechanics. Springer, 1980

    Google Scholar 

  2. Bernstein J., Leites D., Invariant differential operators and irreducible representations of the Lie superalgebra of vector fields, Sel. Math. Sov., v. 1, 1982

    Google Scholar 

  3. Burns D. Jr., Sneider S., Real hypersurfaces in complex manifolds. In: Wells R.O. Jr. (ed.), Proc. Symp. in Pure Math. of the AMS, williams college, 1975. v.30, pt. 1-2, AMS, 1977

    Google Scholar 

  4. Fuchs D., Cohomology of infinite dimensional Lie algebras, Consultunts Bureau, NY, 1987; Feigin B., Fuchs D. Cohomology of Lie groups and Lie algebras. Нтoнн наукн. CoBр. прбА. матeмтн. фунд Напр. 22, BИНИТН. 1988. (Russian, to ap. in English in Springer series Sov.Math. Encycl.)

    Google Scholar 

  5. Ferrara S., Taylor J. (eds.), Supergravity '81. Cambridge Univ. Press, 1982

    Google Scholar 

  6. Freund P. Introduction to supersymmetry. Cambridge Univ. Press, 1986

    Google Scholar 

  7. Fronsdal C., Essays on supersymmetry. D.Reidel, 1986

    Google Scholar 

  8. Goncharov A., Infinitesimal structures related to hermitian symmetric spaces, Funct. Anal. Appl., 15, n3 (1981), 23–24 (Russian); a detailed version see in [G2]

    Google Scholar 

  9. Goncharov A., Generalized conformal structures on manifolds, An enlarged English translation in: [L3], #11 and Selecta Math. Sov. 1987

    Google Scholar 

  10. Galperin A., Ivanov E., Ogievetsky V., Sokachev E., N = 2 supergravity in superspace: different versions and matter couplings. Class. Quantum Grav. 4, 1987, 1255–1265

    Google Scholar 

  11. Galperin A., Ivanov E., Ogievetsky V., Sokachev E., Gauge field geometry from complex and harmonic analiticities I, II. Ann. Phys. 185, #1, 1988, 1–21; 22–45

    Google Scholar 

  12. Galperin A., Nguen Anh Ky, Sokachev E., N = 2 supergravity in superspace: solutions to the constraints and the invariant action. Class. Quantum Grav. 4, 1987, 1235–1253

    Google Scholar 

  13. KacV., Classification of simple {ofZ}-gradedLie superalgebrasandsimpleJordan superalgebras. Commun. Alg. 5(13), 1977, 1375–1400

    Google Scholar 

  14. Leites D., Lie superalgebras, JOSMAR, v. 30, #6, 1984; id. Introduction to Supermanifold theory. Russian Math. Surveys. v.33, nl, 1980, 1–55; an expanded version: [L2]

    Google Scholar 

  15. Leites D., Supermanifold theory. Karelia Branch of the USSR Acad. of Sci., Petrozavodsk, 1983, 200pp. (Russian) = in English a still more expanded version (in 7 volumes) is to be published by Kluwer in 1991–92; meanwhile see the preprinted part in: [L3]

    Google Scholar 

  16. Leites D. (ed.), Seminar on supermanifolds, Reports of Dept. of Math. of Stockholm Univ. n1-34, 2800 pp., 1986–89

    Google Scholar 

  17. Leites D., Selected problems of supermanifold theory. Duke Math. J. v. 54, #2, 1987, 649–656

    Google Scholar 

  18. Leites D., Quantization and supermanifolds. Appendix 3. In: Berezin F., Shubin M., Schroedinger equation. Kluwer, Dordrecht, 1990

    Google Scholar 

  19. Leites D., Kochetkov Yu., Weintrob A., New invariant differential operators and pseudocohomology of supermanifolds and Lie superalgebras. In: Proc. Topological Conf., Staten Island, 1989, Marcel Decker, 1991

    Google Scholar 

  20. Leites D., Poletaeva E., Analogues of the Riemannian structure for classical superspaces. Proc. Intnl. Algebraic Conf. Novosibirsk, 1989. (to appear) (see [L3, #34])

    Google Scholar 

  21. Leites D., Post G., Cohomology to compute. In: Kaltofen E, Watt S.M. eds., Computers and Mathematics, Springer, NY ea, 1989, 73–81

    Google Scholar 

  22. Leites D., Premet A., Structure functions of flag varieties. Geom. Dedicata (to appear)

    Google Scholar 

  23. Leites D., Poletaeva E., Serganova V., Einstein equations on manifolds and supermanifolds (to appear)

    Google Scholar 

  24. Leites D., Poletaeva E., Serganova V., Structure functions on contact supermanifolds (to appear)

    Google Scholar 

  25. McCrimmon K. Jordan algebras and their applications. Bull. Amer. Math. Soc. v.84, n4, 1978, 612–627

    Google Scholar 

  26. Martin Yu., Topics in non-commutative geometry. M.B.Porter lectures. Rice Univ., Dept. of Math., 1989

    Google Scholar 

  27. Manin Yu., Voronov A., Supercell decompositions of flag supervariety. In: лтоги науки. Coвр. пробА. маТeм. НoБeлщиe дocТ. Т.з32, БИНИТН, Moscow, 1988, 125-211 (Russian) Engl. translation in J. Sov. Math. (JOSMAR)

    Google Scholar 

  28. Merkulov S., N = 2 superconformal superspaces. Class. Quantum Grav. 7, 1990, 439–444

    Google Scholar 

  29. Miklashevsky L, Connections, conformal structures and Einstein equation. In: [L3, #27], 1988–9

    Google Scholar 

  30. Ochiai T., Geometry associated with semisimple flat omogeneous spaces, Trans. Amer. Math. Soc., 152, 1970, 159–193

    Google Scholar 

  31. Ogievetsky V.I., Sokachev E.S., The simplest group of Einstein supergravity. Sov. J. Nucl. Phys. v.31, #1, 1980, 264–279

    Google Scholar 

  32. Ogievetsky V.I., Sokachev E.S., The axial gravity superfield and the formalism of the differenrial geometry. Sov. J. Nucl. Phys. v.31, #3, 1980, 821–840

    Google Scholar 

  33. Ogievetsky V., Sokachev E., Supersymmetry and superspace. J.Sov. Math. (JOSMAR) 36, 1987, 721–744 (transl. from Itogi Nauki i Tekhn. Ser. Math. Anal. 22, 1984, 137–173, in Russian)

    Google Scholar 

  34. Onishchik A.L., Vinberg E.B., Seminar on algebraic groups and Lie groups. Springer, Berlin ea, 1990

    Google Scholar 

  35. Poletaeva E., Structure functions on (2, 2)-dimensional supermanifolds with either of the differential forms co+ = dtl(2X-λ)/(1-λ)((1-λ)dpdq + Xdi;dij) or w_ = d4l/X-2(dpdq + dydij), λεC. In: [L3, # 34]

    Google Scholar 

  36. Poletaeva E., Penrose tensors on supergrassmannians. Math. Scand., 1991 (to appear)

    Google Scholar 

  37. Poletaeva E., Serganova V. Structure functions on the usual and exotic symplectic supermanifolds (to appear)

    Google Scholar 

  38. Rosly A.A., Schwarz A.S., Geometry of N = 1 supergravity.I, II. Commun. Math.Phys. 95. 1984, 161–184

    Google Scholar 

  39. Schwarz A.S. Supergravity, complex geometry and G-structures. Commun. Math.Phys. 87. 1982, 37–63

    Google Scholar 

  40. Serganova V. Classification of real simple Lie superalgebras and symmetric superspaces. Funct. Anal. Appl. 17, #3, 1983, 46–54

    Google Scholar 

  41. Shander V., Analogues of the Frobenius and Darboux theorems for supermanifolds. C. R. de l'Acad. bulg. de Sci., t. 36, #3, 1983, 309–312

    Google Scholar 

  42. Shchepochkina I., Exceptional infinite dimensional Lie superalgebras of vector fields. C. R. de l'Acad. bulg. de Sci., t. 36, #3, 1983, 313–314 (Russian)

    Google Scholar 

  43. Sokachev E. Off-shell six-dimensional supergravity in harmonic superspace Class. Quantum Grav. 5, 1459–1471, 1988

    Google Scholar 

  44. Sternberg S. Lectures on differential geometry, 2nd ed, Chelsey, 1985

    Google Scholar 

  45. Tanaka N., On infinitesimal automorphisms of Siegel domains, J. Math. Soc. Japan 22, 1970, 180–212.

    Google Scholar 

  46. Problems of nuclear physics and cosmic rays. v.24, Kharkov, Бнща щкoАа, 1985 (Russisan) Festschrift on the occation of D.Volkov's birthday.

    Google Scholar 

  47. Weintrob A. Almost complex structures on supermanifolds. Questions of group theory and homological algebra., Yaroslavl Univ. Press, Yaroslavl, 1985, 1 (Russian) = English translation in [L3, n24]

    Google Scholar 

  48. West P. Introduction to supersymmetry and supergravity. World Sci., Singapore, 1986

    Google Scholar 

  49. Wess J., Bagger J., Supersymmetry and supergravity. Princeton Univ. Press, 1983

    Google Scholar 

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Author information

Authors and Affiliations

  1. SFB-170, Dept of Math., Göttingen

    D. Leites (speaker)

  2. Department of Mathematics, Yale Univ., New Haven, CT, USA

    V. Serganova

  3. Dept of Math. UConn., Storrs, CT, USA

    G. Vinel

Authors
  1. D. Leites
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  2. V. Serganova
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  3. G. Vinel
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Editor information

C. Bartocci U. Bruzzo R. Cianci

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© 1991 Springer-Verlag

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Leites, D., Serganova, V., Vinel, G. (1991). Classical superspaces and related structures. In: Bartocci, C., Bruzzo, U., Cianci, R. (eds) Differential Geometric Methods in Theoretical Physics. Lecture Notes in Physics, vol 375. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53763-5_66

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  • DOI: https://doi.org/10.1007/3-540-53763-5_66

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  • Print ISBN: 978-3-540-53763-2

  • Online ISBN: 978-3-540-47090-8

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