Hiroshima Mathematical Journal

The conformal factor and a central extension of a formal loop group with values in ${\rm PSL}(2,{\bf R})$

Ryuichi Sawae

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Hiroshima Math. J., Volume 23, Number 2 (1993), 249-303.

First available in Project Euclid: 21 March 2008

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Primary: 83C20: Classes of solutions; algebraically special solutions, metrics with symmetries
Secondary: 20N05: Loops, quasigroups [See also 05Bxx] 22E67: Loop groups and related constructions, group-theoretic treatment [See also 58D05] 22E70: Applications of Lie groups to physics; explicit representations [See also 81R05, 81R10]


Sawae, Ryuichi. The conformal factor and a central extension of a formal loop group with values in ${\rm PSL}(2,{\bf R})$. Hiroshima Math. J. 23 (1993), no. 2, 249--303. doi:10.32917/hmj/1206128253. https://projecteuclid.org/euclid.hmj/1206128253

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  • [1] P. Breitenlohner and D. Maison, On the Geroch group, Ann. Inst. Henri Poincare 46 (1987), 215-246.
  • [2] H. Doi and K. Okamoto, A survey of the generalized Geroch conjecture, Adv. Stud, in Pure Math. 14 (1988), 379-393.
  • [3] H. Doi and R. Sawae, A linearization of the Einstein-Maxwell field equations, Hiroshima Math. J. 20 (1990), 515-524.
  • [4] H. Doi and R. Sawae, Chiral models and the Einstein-Maxwell field equations, Hiroshima Math. J. 20 (1990), 651-656.
  • [5] F. J. Ernst, New formulation of the axially symmetric gravitational field problem II, Phys. Rev. 168 (1968), 1415-1417.
  • [6] R. Geroch, A method for generating new solutions of Einstein's equations II, J. Math. Phys. 13 (1972), 394-404.
  • [7] T. Hasimoto and R. Sawae, A Linearization of S(U(1) x 17(2))\517(1, 2) -model, to appear in Hiroshima Math. J.
  • [8] I. Hauser and F. J. Ernst, Proof of a generalized Geroch conjecture, in "Galaxies axisymmetric systems and relativity edited by M. A. H. MacCallum," Cambridge Univ. Press 115, Cambridge, 1985.
  • [9] B. Julia, in Superspace and Supergravity, S. Hawking and M. Roek eds., Springer-Verlag (1985), 329-352.
  • [10] V. G. Kac, "Infinite Dimensional Lie Algebras," Birkhauser, 1975.
  • [11] W. Kinnersley, Symmetries of the stationary Einstein-Maxwell field equations I, J. Math. Phys. 18 (1977), 1529-1537.
  • [12] A. W. Knapp, "Representation theory of semisimple groups --An overview based on examples," Princeton Univ. Press, Princeton, 1986.
  • [13] L. D. Landau and E. M. Lifshit, "The classical theory of fields, Fourth revised English edition," Pergamon press, 1975.
  • [14] K. Nagatomo, The Ernst equation as a motion on a universal Grassmann manifold, Commun. Math. Phys. 122 (1989), 423-453.
  • [15] Y. Nakamura, On a linearisation of the satationary axially symmetric Einstein equations, Class. Quantum Grav. 4 (1987), 437-440.
  • [16] K. Okamoto, in Proceedings of Workshop on Beyond Riemann Surfaces, R. Kubo ed., RITP Hiroshima Univ. (1989), 61-67.
  • [17] private communications with K. Okamoto and K. Takasaki.
  • [18] K. Takasaki, A new approach to the self-dual Yang-Mills equations II, Saitama Math. J. 3 (1985), 11-40.
  • [19] V. S. Varadarajan, "Lie groups, Lie algebras, and their representations," Springer-Verlag, 1984.
  • [20] H. Weyl, Zur Gravitationstheorie, Ann. der Phys. 54 (1917), 117-145.
  • [21] Y. S. Wu and M. L. Ge, in Vertex Operators in Mathematics and Physics, J. Lepowsky, S. Mandelstam and I. M. Singer eds., Springer-Verlag (1985), 329-352.