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The Sylvester's law of inertia in simple graded Lie algebras
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1998 Volume 50 Issue 3 Pages 593-614
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- Published: 1998 Received: August 15, 1996 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Ichiro Satake on the occasion of his seventieth
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) H. Asano and S. Kaneyuki, On compact generalized Jordan triple systems of the second kind, Tokyo J. Math., 11 (1988), 105-118.
2) N. Bourbaki, Groupes et Algèbres de Lie, Chapitre 4, 5 et 6, Masson, Paris, 1981.
3) H. Braun and M. Koecher, Jordan-Algebren, Springer, Berlin, Heidelberg, New York, 1966.
4) J. E. D'Atri and S. Gindikin, Siegel domain realization of pseudo-Hermitian symmetric manifolds, Geometriae Dedicata, 46 (1993), 91-125.
5) J. Faraut and S. Gindikin, Pseudo-Hermitian symmetric spaces of tube type, in Topics in Geometry, Honoring the Memory of Joe D'Atri, Birkhäuser, Boston-Basel-Berlin, 1996, 123-154.
6) S. Gindikin and S. Kaneyuki, On the automorphism group of the generalized conformal structure of a symmetric R-space, Differential Geometry and its Applications, 8 (1998), 21-33.
7) S. Kaneyuki, On orbit structure of compactifications of parahermitian symmetric spaces, Japan. J. Math., 13 (1987), 333-370.
8) S. Kaneyuki, A decomposition theorem for simple Lie groups associated with parahermitian symmetric spaces, Tokyo J. Math., 10 (1987), 363-373.
9) S. Kaneyuki, The Sylvester's law of inertia for Jordan algebras, Proc. Japan Acad., Ser. A, 64 (1988), 311-313.
10) S. Kaneyuki, On the causal structures of Šilov boundaries of symmetric bounded domains, in Prospects in Complex Geometry, Lect. Notes in Math., 1468, Springer, Berlin-Heidelberg-New York, 1991,127-159.
11) S. Kaneyuki, Pseudo-hermitian symmetric spaces and Siegel domains over nondegenerate cones, Hokkaido Math. J., 20 (1991), 213-239.
12) S. Kaneyuki, On the subalgebras g0 and gev, of semisimple graded Lie algebras, J. Math. Soc. Japan, 45 (1993), 1-19.
13) S. Kaneyuki and H. Asano, Graded Lie algebras and generalized Jordan triple systems, Nagoya Math. J., 112 (1988), 81-115.
14) S. Kobayashi and T. Nagano, On filtered Lie algebras and geometric structures I, J. Math. Mech., 13 (1964), 875-908.
15) M. Koecher, Positivitätsbereiche im Rn, Amer. J. Math., 79 (1957), 575-596.
16) M. Koecher, Jordan Algebras and their Applications, Lect. Notes, Univ. of Minnesota, Minneapolis, 1962.
17) O. Loos, Jordan triple systems, R-spaces and bounded symmetric domains, Bull. Amer. Math. Soc., 77 (1971), 558-561.
18) O. Loos, Bounded Symmetric Domains and Jordan Pairs, Math. Lect. Univ. Calif., Irvine, 1977.
19) H. Matsumoto, Quelques remarques sur les groupes de Lie algébriques réels, J. Math. Soc. Japan, 16 (1964), 419-446.
20) T. Oshima and J. Sekiguchi, The restricted root system of a semisimple symmetric pair, in Group Representations and Systems of Differential Equations, Adv. Studies in Pure Math., 4, Kinokuniya, Tokyo and North-Holland, Amsterdam, 1984, 433-497.
21) I. Satake, Algebraic Structures of Symmetric Domains, Iwanami Shoten, Tokyo and Princeton Univ. Press, Princeton, 1980.
22) I. Satake, A formula in simple Jordan algebras, Tohoku Math. J., 36 (1984), 611-622.
23) I. Satake, On zeta functions associated with self dual homogeneous cones, in Reports on Symposium of Geometry and Automorphic Functions, Tohoku Univ., Sendai, 1988, 145-168.
24) H. Shima, Symmetric spaces with invariant locally Hessian structures, J. Math. Soc. Japan, 29 (1977), 581-589.
25) M. Takeuchi, Cell decompositions and Morse equalities on certain symmetric spaces, J. Fac. Sci. Univ. Tokyo, 12 (1965), 81-192.
26) M. Takeuchi, On conjugate loci and cut loci of compact symmetric spaces II, Tsukuba J. Math., 3 (1979), 1-29.
27) M. Takeuchi, Basic transformations of symmetric R-spaces, Osaka J. Math., 25 (1988), 259-297.
28) N. Tanaka, On nondegenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan. J. Math., 2 (1976), 131-190.
29) E. B. Vinberg, Homogeneous cones, Dokl. Akad. Nauk, SSSR, 133 (1960), 9-12.
Right : [1] H. Asano and S. Kaneyuki, On compact generalized Jordan triple systems of the second kind, Tokyo J. Math., 11 (1988), 105-118.
[2] N. Bourbaki, Groupes et Algèbres de Lie, Chapitre 4, 5 et 6, Masson, Paris, 1981.
[3] H. Braun and M. Koecher, Jordan-Algebren, Springer, Berlin, Heidelberg, New York, 1966.
[4] J. E. D'Atri and S. Gindikin, Siegel domain realization of pseudo-Hermitian symmetric manifolds, Geometriae Dedicata, 46 (1993), 91-125.
[5] J. Faraut and S. Gindikin, Pseudo-Hermitian symmetric spaces of tube type, in Topics in Geometry, Honoring the Memory of Joe D'Atri, Birkhäuser, Boston-Basel-Berlin, 1996, 123-154.
[6] S. Gindikin and S. Kaneyuki, On the automorphism group of the generalized conformal structure of a symmetric R-space, Differential Geometry and its Applications, 8 (1998), 21-33.
[7] S. Kaneyuki, On orbit structure of compactifications of parahermitian symmetric spaces, Japan. J. Math., 13 (1987), 333-370.
[8] S. Kaneyuki, A decomposition theorem for simple Lie groups associated with parahermitian symmetric spaces, Tokyo J. Math., 10 (1987), 363-373.
[9] S. Kaneyuki, The Sylvester's law of inertia for Jordan algebras, Proc. Japan Acad., Ser. A, 64 (1988), 311-313.
[10] S. Kaneyuki, On the causal structures of Šilov boundaries of symmetric bounded domains, in Prospects in Complex Geometry, Lect. Notes in Math., 1468, Springer, Berlin-Heidelberg-New York, 1991,127-159.
[11] S. Kaneyuki, Pseudo-hermitian symmetric spaces and Siegel domains over nondegenerate cones, Hokkaido Math. J., 20 (1991), 213-239.
[12] S. Kaneyuki, On the subalgebras g0 and gev, of semisimple graded Lie algebras, J. Math. Soc. Japan, 45 (1993), 1-19.
[13] S. Kaneyuki and H. Asano, Graded Lie algebras and generalized Jordan triple systems, Nagoya Math. J., 112 (1988), 81-115.
[14] S. Kobayashi and T. Nagano, On filtered Lie algebras and geometric structures I, J. Math. Mech., 13 (1964), 875-908.
[15] M. Koecher, Positivitätsbereiche im Rn, Amer. J. Math., 79 (1957), 575-596.
[16] M. Koecher, Jordan Algebras and their Applications, Lect. Notes, Univ. of Minnesota, Minneapolis, 1962.
[17] O. Loos, Jordan triple systems, R-spaces and bounded symmetric domains, Bull. Amer. Math. Soc., 77 (1971), 558-561.
[18] O. Loos, Bounded Symmetric Domains and Jordan Pairs, Math. Lect. Univ. Calif., Irvine, 1977.
[19] H. Matsumoto, Quelques remarques sur les groupes de Lie algébriques réels, J. Math. Soc. Japan, 16 (1964), 419-446.
[20] T. Oshima and J. Sekiguchi, The restricted root system of a semisimple symmetric pair, in Group Representations and Systems of Differential Equations, Adv. Studies in Pure Math., 4, Kinokuniya, Tokyo and North-Holland, Amsterdam, 1984, 433-497.
[21] I. Satake, Algebraic Structures of Symmetric Domains, Iwanami Shoten, Tokyo and Princeton Univ. Press, Princeton, 1980.
[22] I. Satake, A formula in simple Jordan algebras, Tohoku Math. J., 36 (1984), 611-622.
[23] I. Satake, On zeta functions associated with self-dual homogeneous cones, in Reports on Symposium of Geometry and Automorphic Functions, Tohoku Univ., Sendai, 1988, 145-168.
[24] H. Shima, Symmetric spaces with invariant locally Hessian structures, J. Math. Soc. Japan, 29 (1977), 581-589.
[25] M. Takeuchi, Cell decompositions and Morse equalities on certain symmetric spaces, J. Fac. Sci. Univ. Tokyo, 12 (1965), 81-192.
[26] M. Takeuchi, On conjugate loci and cut loci of compact symmetric spaces II, Tsukuba J. Math., 3 (1979), 1-29.
[27] M. Takeuchi, Basic transformations of symmetric R-spaces, Osaka J. Math., 25 (1988), 259-297.
[28] N. Tanaka, On nondegenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan. J. Math., 2 (1976), 131-190.
[29] E. B. Vinberg, Homogeneous cones, Dokl. Akad. Nauk, SSSR, 133 (1960), 9-12.
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