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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Graded Lie algebras of the second kind
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by Jih Hsin Chêng PDF
Trans. Amer. Math. Soc. 302 (1987), 467-488 Request permission

Abstract:

The associated Lie algebra of the Cartan connection for an abstract CR-hypersurface admits a gradation of the second kind. In this article, we give two ways to characterize this kind of graded Lie algebras, namely, geometric characterization in terms of symmetric spaces and algebraic characterization in terms of root systems. A complete list of this class of Lie algebras is given.
References
    E. Cartan, Sur la géométrie pseudo-conforme des hypersurfaces de deux variables complexes. I, II, Oeuvres II, 2, pp. 1231-1304; ibid. III, 2, pp. 1217-1238.
  • S. S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219–271. MR 425155, DOI 10.1007/BF02392146
  • Sigurdur Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 514561
  • James E. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, Vol. 9, Springer-Verlag, New York-Berlin, 1972. MR 0323842, DOI 10.1007/978-1-4612-6398-2
  • Shoshichi Kobayashi and Tadashi Nagano, On filtered Lie algebras and geometric structures. I, J. Math. Mech. 13 (1964), 875–907. MR 0168704
  • O. Loos, Symmetric spaces. II, Benjamin, New York. 1969.
  • Noboru Tanaka, On the pseudo-conformal geometry of hypersurfaces of the space of $n$ complex variables, J. Math. Soc. Japan 14 (1962), 397–429. MR 145555, DOI 10.2969/jmsj/01440397
  • Noboru Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan. J. Math. (N.S.) 2 (1976), no. 1, 131–190. MR 589931, DOI 10.4099/math1924.2.131
  • Joseph A. Wolf, Complex homogeneous contact manifolds and quaternionic symmetric spaces, J. Math. Mech. 14 (1965), 1033–1047. MR 0185554
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 302 (1987), 467-488
  • MSC: Primary 17B70; Secondary 32F25, 53C35
  • DOI: https://doi.org/10.1090/S0002-9947-1987-0891630-X
  • MathSciNet review: 891630