Lie groups and subsemigroups with surjective exponential function

Memoirs of the American Mathematical Society

Volumn , Issue 618, 1997, Pages 1-172

  Hofmann, Karl H ^a   Ruppert, Wolfgang A F ^b  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

^b UNIVERSITY OF NATURAL RESOURCES AND LIFE SCIENCES   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002319619     PISSN: 00659266     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (84)

1. A. Borel, Linear Algebraic Groups, W. A. Benjamin, New York, N. Y., 1969.
2. N. Bourbaki, Intégration, Chap. 8, Hermann, Paris, 1961.
3. -, Groupes et algèbres de Lie, Chap. 1, Hermann, Paris, 1960.
4. -, Groupes et algèbres de Lie, Chap. 2 et 3, Hermann, Paris, 1972.
5. -, Groupes et algèbres de Lie, Chap. 7 et 8, Hermann, Paris, 1975.
6. -, Variétés différentielles et analytiques, Diffusion CCLS, Paris, 1982.
7. P. B. Chen and T. S. Wu, On exponential groups, J. Pure Appl. Algebra 93 (1994), 169-178.
8. C. Chevalley, Théorie des groupes de Lie III, Hermann, Paris, 1955.
9. L. Corwin and M. Moskowitz, A note on the exponential map of a real or p-adic Lie group, J. of Pure Appl. Alg. 96 (1994), 113-132.
10. J. Dixmier, L'application exponentielle dans les groupes de Lie résolubles, Bull. Soc. Math. France 85 (1957), 113-121.
11. -, Sur les espaces localement quasi-compacts, Can. J. Math., 20 (1968), 1093-1100.
12. N. Dörr, A note on the oscillator group (1992), 31-38.
13. D. Ž. Djoković, On the exponential map in classical Lie groups (1980), 76-88.
14. D. Ž. Doković, The interior and the exterior of the image of the exponential map in classical Lie groups (1988), 90-109.
15. -, The exponential image of simple complex Lie groups of exceptional type (1988), 101-111.
16. D. Ž. Doković and Nguyen Q. Thǎńg, On the exponential map of almost simple real algebraic groups, J. of Lie Theory 5 (1995), 275-291.
17. -, Lie groups with dense exponential image, Math. Z., to appear.
18. A. Eggert, Zur Klassifikation von Semialgebren, (Dissertation, TH Darmstadt 1991) Mitt. Math. Sem. Giessen, vol. 204, Universität Giessen, Giessen, 1991.
19. R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989.
20. J. M. G. Fell, A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff space (1962), 472-476.
21. G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. Scott, A Compendium of Continuous Latices, Springer, Berlin etc., 1980.
22. V.M. Gichev, On the structure of Lie algebras admitting and invariant cone, Semigroups in Algebra, Geometry, and Analysis (K. H. Hofmann, J. D. Lawson, and E. B. Vinberg, eds.), De Gruyter Expositions in Mathematics 20, De Gruyter, Berlin etc., 1995, pp. 107-120.
23. M. Goto, Index of the exponential map of a semialgebraic group, J. Math. Soc. Japan 29 (1997), 161-163.
24. S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, Boston etc, 1978.
25. H. Heyer, Probability Measurs on Locally Compact Groups, Springer, Berlin etc. 1977.
26. J. Hilgert and K. H. Hofmann, Semigroups in Lie groups, semialgebras in Lie algebras (1985), 481-504.
27. J. Hilgert, K. H. Hofmann, and J. D. Lawson, Lie groups, convex cones and semigroups, Oxford Science Publications, Clarendon Press, Oxford, 1989.
28. J. Hilgert, K.-H. Neeb, Lie Semigroups and their Applications, Lecture Notes in Mathematics, vol. 1552, Springer, Berlin etc., 1993.
29. G. Hochschild, The Strucutre of Lie Groups, Holden-Day, San Francisco etc, 1965.
30. K. H. Hofmann, Hyperplane subalgebras of real Lie algebras (1990), 207-224.
31. -, A memo on singularities, Memorandum circulated at Technische Hochschule Darmstadt 1990.
32. -, A memo on the exponential functional and regular points (1992), 24-37.
33. -, Near Cartan algebras and groups (1992), 135-151.
34. -, The hyperspace of a locally compact space, Preprint THD, Darmstadt 1994.
35. K. H. Hofmann and J. D. Lawson, Foundations of Lie semigroups, Springer-Verlag, Berlin etc, 1983, pp. 128-201.
36. -, Divisible subsemigroups of Lie gropus (1983), 427-437.
37. K. H. Hofmann, J. D. Lawson, and J. S. Pym, The Analytical Theory of Semigroups: Trends and Developments, De Gruyter Expositions in Mathematics 1, De Gruyter, Berlin etc., 1990.
38. K. H. Hofmann, J. D. Lawson, and W. A. F. Ruppert, On finiteness theorems and procupine varieties in Lie algebras (1993), 49-63.
39. -, Weyl groups are finite - and other finiteness properties of Cartan subalgebras, Math. Nachr. 179 (1996), to appear.
40. K. H. Hofmann, J. D. Lawson, and E. B. Vinberg, Semigroups in Algebra, Geometry, and Analysis, De Gruyter Expositions in Mathematics 20, De Gruyter, Berlin etc., 1995.
41. K. H. Hofmann and P. S. Mostert, Elements of Compact Semigroups, Charles E. Merrill, Columbus, Ohio, 1966.
42. K. H. Hofmann and A. Mukherjea, On the density of the image of the exponential function, Math. Ann. 234 (1978), 263-273.
43. K. H. Hofmann and W. A. F. Rupert, On the interior of subsemigroups of Lie groups, Trans. Amer. Math. Soc. 324 (1991), 169-179.
44. -, The divisibility problem for subsemigroups of Lie groups, Seminar Sophus Lie 1 (1991), 205-213.
45. -, The structure of Lie groups which support closed divisible subsemigroups, Semigroups with Applications (J. M. Howie, W. D. Munn, and H.-J. Weinert, eds.), World Scientific, Singapore, 1992, pp. 11-30.
46. -, On Porcupine Varieties in Lie Algebras, Math. Annalen, 298 (1994), 403-425.
47. -, Lie groups and exponential Lie subsemigroups, Semigroups in Algebra, Geometry, and Analysis (K. H. Hofmann, J. D. Lawson, and E. B. Vinberg, eds.), De Gruyter Expositions in Mathematics 20, De Gruyter, Berlin etc., 1995, pp. 159-198.
48. K. H. Hofmann and F. Watkins, The spectrum as a functor, Continuous Lattices, Proceedings Bremen 1979, Lecture Notes in Math., (B. Banaschewski and R.-E. Hoffmann, eds.), vol. 871, Springer-Verl., Berlin etc., 1981, pp. 249-263.
49. W. Jaworski, The density of the image of the exponential function and spacious locally compact groups, J. of Lie Theory 5 (1995), 129-134.
50. V. Jurdevic and I. Kupka, Control systems on semisimple Lie groups and their homogeneous spaces (1981), 151-179.
51. H.-L. Lai, Surjectivity of exponential map on semisimple Lie groups, J. Math. Soc. 29 (1977), 303-325.
52. -, On the singularity of the exponential map on a Lie group, Proc. Amer. Math. Soc. 62 (1977), 334-336.
53. -, Index of the exponential map of a center-free complex simple Lie group, Osaka J. Math. 15 (1978), 553-560.
54. -, Index of the exponential map on a complex simple Lie group, Osaka J. Math. 15 (1978), 561-567.
55. -, Corrections and supplements to "Index of the exponential map on a complex simple Lie group", Osaka J. Math. 17 (1980), 525-530.
56. -, Index of a simple adjoint group, Bull. Inst. Math. Acad. Sinica 8 (1980), 603-608.
57. -, Exponential map on a simple group of classical type, Bull. Inst. Math. Acad. Sinica 10 (1982), 417-430.
58. L. Markus, Exponentials in algebraic matrix groups, Adv. Math. 11 (1973), 351-367.
59. M. McCrudden, On n-th roots and infinitely divisible elements in a connected Lie group (1981), 293-299.
60. D. Mittenhuber, Spacious Lie groups, J. of Lie Theory 5 (1995), 135-146.
61. D. Mittenhuber and K.-H. Neeb, On the exponential function of an invariant Lie semigroup (1992), 21-30.
62. -, Remarks on our paper "On the exponential function of an invariant Lie semigroup" (1993), 119-120.
63. Z. I. Moskalenko, Exponential groups and ML-groups, Ukrain. Mat. Zhurnal 28 (1976), 501-510.
64. M. Moskowitz, The surjectivity of the exponential map for certain Lie groups, Ann. Mat. Pura Appl., Ser. 4 166 (1994), 129-143.
65. -, Correction to "The surjectivity of the exponential map for certain Lie groups", Ann. Mat. Pura. Appl., to appear.
66. -, Exponentiality of algebraic groups, submitted.
67. M. Moskowitz and M. Wüstner, Exponentiality of certain real solvable Lie groups, submitted.
68. K.-H. Neeb, Semigroups in the Universal Covering of S1(2) (1991), 33-43.
69. -, On the foundations of Lie semigroups (1992), 165-189.
70. -, A topology on the space of closed subsets, Interdepartmental Memo 1992, 16pp.
71. -, Invariant Subsemigroups of Lie Groups, Memoirs pf the Amer. Math. Soc., vol. 499, American Mathematical Scoiety, Providence R. I., 1993.
72. -, Weakly exponential Lie groups, J. of Algebra 179 (1996), 331-361.
73. M. Nishikawa, Exponential image in the real general linear group, Bull. Fukuoka Univ. Ed. III 26 (1976), 35-44.
74. -, Exponential image in the real special linear group, Bull. Fukuoka Univ. Ed. III 28 (1978), 1-6.
75. 0, Mem. Fac. Sci. Kyushu Univ. Ser. A 37 (1983), 63-69.
76. -, Exponential image and conjugacy classes in the group O(3, 2), Hiroshima Math. J. 14 (1984), 311-332.
77. M. Saito, Sur certains groupes de Lie résolubles (1957), 1-11, and 157-168.
78. L. San Martin, Nonreversibility of subsemigroups of semisimple Lie groups (1992), 376-387.
79. J. Tits, Tabellen zu den einfachen Liegruppen und ihren Darstellungen, Lecture Notes in Math., 40, Springer, Berlin etc, 1967.
80. M. Wüstner, Beiträge zur Struktur Theorie auflösbarer Lie Gruppen, (Dissertation, TH Darmstadt 1995), TH Darmstadt, 1995.
81. -, A connected complex simple centerfree Lie group whose exponential function is not surjective, J. of Lie Theory 5 (1995), 203-205.
82. -, On the surjectivtty of the exponential function of complex algebraic, complex semisimple, and complex splittable Lie groups, J. of Alg., to appear.
83. -, On the surjectivity of the exponential function of solvable Lie groups, Math. Nachrichten, to appear.
84. -, On the exponential function of real splittable and real semisimple Lie groups, in preparation.