대한수학회지 (Journal of the Korean Mathematical Society)

  • 제43권3호
  • /
  • Pages.507-528
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  • 2006
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  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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JORDAN AUTOMORPHIC GENERATORS OF EUCLIDEAN JORDAN ALGEBRAS

  • Kim, Jung-Hwa (Department of Mathematics Kyungpook National University) ;
  • Lim, Yong-Do (Department of Mathematics Kyungpook National University)
  • 발행 : 2006.05.01
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초록

In this paper we show that the Koecher's Jordan automorphic generators of one variable on an irreducible symmetric cone are enough to determine the elements of scalar multiple of the Jordan identity on the attached simple Euclidean Jordan algebra. Its various geometric, Jordan and Lie theoretic interpretations associated to the Cartan-Hadamard metric and Cartan decomposition of the linear automorphisms group of a symmetric cone are given with validity on infinite-dimensional spin factors

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참고문헌

  1. W. Bertram, The geometry of Jordan and Lie structures, Lecture Notes in Math- ematics, 1754. Springer-Verlag, Berlin, 2000
  2. J. Faraut and A. Koranyi, Analysis on symmetric cones, Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford Univer- sity Press, New York, 1994
  3. L. Faybusovich, A Jordan-algebraic approach to potential-reduction algorithms, Math. Z. 239 (2002), no. 1, 117-129 https://doi.org/10.1007/s002090100286
  4. L. Faybusovich and T. Tsuchiya, Primal-dual algorithms and infinite-dimen-sional Jordan algebras of finite rank, Math. Program. 97 (2003), no. 3, Ser. B, 471-493 https://doi.org/10.1007/s10107-003-0424-4
  5. M. Fiedler and V. Ptak, A new positive definite geometric mean of two positive definite matrices, Linear Algebra Appl. 251 (1997), 1-20 https://doi.org/10.1016/0024-3795(95)00540-4
  6. R. A. Hauser, Self-scaled barriers for semidefinite programming, Numerical Anal- ysis Report DAMTP 2000/NA02, Department of Applied Mathematics and The- oretical Physics, Silver Street, Cambridge, England CB3 9EW, March 2000
  7. R. A. Hauser and O. Guler, Self-scaled barrier functions on symmetric cones and their classification, Found. Comput. Math. 2 (2002), no. 2, 121-143 https://doi.org/10.1007/s102080010022
  8. R. A. Hauser and Y. Lim, Self-scaled barriers for irreducible symmetric cones, SIAM J. Optim. 12 (2002), no. 3, 715-723 https://doi.org/10.1137/S1052623400370953
  9. A. Kalliterakis, Estimations a l'infini des fonctions de Bessel associees aux repre- sentations d'une algebre de Jordan, J. Lie Theory 11 (2001), no. 2, 273-303
  10. W. Kaup, Jordan algebras and holomorphy, Functional analysis, holomorphy, and approximation theory, Lecture Notes in Math., 843, Springer, Berlin, 1981
  11. M. Koecher, The Minnesota notes on Jordan algebras and their applications, Edited, annotated and with a preface by Aloys Krieg and Sebastian Walcher, Lecture Notes in Mathematics, 1710. Springer-Verlag, Berlin, 1999
  12. B. Kostant, On convexity, the Weyl group and the Iwasawa decomposition, Ann. Sci. Ecole Norm. Sup. (4) 6 (1973), 413-455 (1974)
  13. O. Kowalski, Generalized symmetric spaces, Lecture Notes in Mathematics, 805. Springer-Verlag, Berlin-New York, 1980
  14. S. Lang, Fundamentals of differential geometry, Graduate Texts in Mathematics, 191. Springer-Verlag, New York, 1999
  15. J. D. Lawson and Y. Lim, The geometric mean, matrices, metrics, and more, Amer. Math. Monthly 108 (2001), no. 9, 797-812 https://doi.org/10.2307/2695553
  16. J. D. Lawson and Y. Lim, Means on dyadic symmetric sets and polar decompositions, Abh. Math. Sem. Univ. Hamburg 74 (2004), 135-150 https://doi.org/10.1007/BF02941530
  17. Y. Lim, Geometric means on symmetric cones, Arch. Math. (Basel) 75 (2000), no. 1, 39-45 https://doi.org/10.1007/s000130050471
  18. Y. Lim, Applications of geometric means on symmetric cones, Math. Ann. 319 (2001), no. 3, 457-468 https://doi.org/10.1007/PL00004442
  19. Y. Lim, Best approximation in Riemannian geodesic submanifolds of positive definite matrices, Canad. J. Math. 56 (2004), no. 4, 776-793 https://doi.org/10.4153/CJM-2004-035-5
  20. Y. Lim, J. Kim, and L. Faybusovich, Simultaneous diagonalization on simple Euclidean Jordan algebras and its applications, Forum Math. 15 (2003), no. 4, 639-644 https://doi.org/10.1515/form.2003.034
  21. K. -H. Neeb, A Cartan-Hadamard theorem for Banach-Finsler manifolds, Geom. Dedicata 95 (2002), 115-156 https://doi.org/10.1023/A:1021221029301
  22. W. Rudin, Functional analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Dusseldorf-Johannesburg, 1973
  23. H. Upmeier, Symmetric Banach manifolds and Jordan C*-algebras, North- Holland Mathematics Studies, 104, North-Holland Publishing Co., Amsterdam, 1985