An exposition of the structure of solvmanifolds. Part I: Algebraic theory
HTML articles powered by AMS MathViewer
- by Louis Auslander PDF
- Bull. Amer. Math. Soc. 79 (1973), 227-261
References
- Louis Auslander, On radicals of discrete subgroups of Lie groups, Amer. J. Math. 85 (1963), 145–150. MR 152607, DOI 10.2307/2373206
- Louis Auslander, Bieberbach’s theorem on space groups and discrete uniform subgroups of Lie groups. II, Amer. J. Math. 83 (1961), 276–280. MR 123637, DOI 10.2307/2372956
- Louis Auslander, Solvable Lie groups acting on nilmanifolds, Amer. J. Math. 82 (1960), 653–660. MR 122909, DOI 10.2307/2372933
- L. Auslander and L. W. Green, $G$-induced flows, Amer. J. Math. 88 (1966), 43–60. MR 199308, DOI 10.2307/2373046
- L. Auslander and J. Brezin, Almost algebraic Lie algebras, J. Algebra 8 (1968), 295–313. MR 224745, DOI 10.1016/0021-8693(68)90061-6
- Louis Auslander, Fundamental groups of compact solvmanifolds, Amer. J. Math. 82 (1960), 689–697. MR 122910, DOI 10.2307/2372935
- Louis Auslander, On a problem of Philip Hall, Ann. of Math. (2) 86 (1967), 112–116. MR 218454, DOI 10.2307/1970362
- L. Auslander and R. Tolimieri, Splitting theorems and the structure of solvmanifolds, Ann. of Math. (2) 92 (1970), 164–173. MR 276995, DOI 10.2307/1970700
- Louis Auslander, An account of the theory of crystallographic groups, Proc. Amer. Math. Soc. 16 (1965), 1230–1236. MR 185012, DOI 10.1090/S0002-9939-1965-0185012-7
- Louis Auslander, Discrete uniform subgroups of solvable Lie groups, Trans. Amer. Math. Soc. 99 (1961), 398–402. MR 131490, DOI 10.1090/S0002-9947-1961-0131490-X
- Louis Auslander, A characterization of discrete solvable matrix groups, Bull. Amer. Math. Soc. 67 (1961), 235–236. MR 123620, DOI 10.1090/S0002-9904-1961-10587-9
- L. Auslander and M. Auslander, Solvable Lie groups and locally euclidean Riemann spaces, Proc. Amer. Math. Soc. 9 (1958), 933–941. MR 103240, DOI 10.1090/S0002-9939-1958-0103240-X
- L. Auslander and R. Tolimieri, On a conjecture of G. D. Mostow and the structure of solvmanifolds, Bull. Amer. Math. Soc. 75 (1969), 1330–1333. MR 254870, DOI 10.1090/S0002-9904-1969-12416-X
- Louis Auslander, The automorphism group of a polycyclic group, Ann. of Math. (2) 89 (1969), 314–322. MR 271202, DOI 10.2307/1970671 15. L. Auslander, On a problem of Philip Hall (unpublished notes).
- Louis Auslander, Some compact solvmanifolds and locally affine spaces, J. Math. Mech. 7 (1958), 963–975. MR 0101280, DOI 10.1512/iumj.1958.7.57056
- L. Auslander, L. Green, and F. Hahn, Flows on homogeneous spaces, Annals of Mathematics Studies, No. 53, Princeton University Press, Princeton, N.J., 1963. With the assistance of L. Markus and W. Massey, and an appendix by L. Greenberg. MR 0167569, DOI 10.1515/9781400882021
- Garrett Birkhoff, Representability of Lie algebras and Lie groups by matrices, Ann. of Math. (2) 38 (1937), no. 2, 526–532. MR 1503351, DOI 10.2307/1968569
- Armand Borel, Linear algebraic groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. Notes taken by Hyman Bass. MR 0251042
- J. Dixmier, L’application exponentielle dans les groupes de Lie résolubles, Bull. Soc. Math. France 85 (1957), 113–121 (French). MR 92930, DOI 10.24033/bsmf.1483
- Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0143793
- R. Warren Johnson, Presentations of solvmanifolds, Amer. J. Math. 94 (1972), 82–102. MR 301752, DOI 10.2307/2373595
- A. I. Mal′cev, On a class of homogeneous spaces, Izvestiya Akad. Nauk. SSSR. Ser. Mat. 13 (1949), 9–32 (Russian). MR 0028842
- A. I. Malcev, Solvable Lie algebras, Amer. Math. Soc. Translation 1950 (1950), no. 27, 36. MR 0037292
- A. I. Mal′cev, On some classes of infinite soluble groups, Mat. Sbornik N.S. 28(70) (1951), 567–588 (Russian). MR 0043088
- Calvin C. Moore, Decomposition of unitary representations defined by discrete subgroups of nilpotent groups, Ann. of Math. (2) 82 (1965), 146–182. MR 181701, DOI 10.2307/1970567
- G. D. Mostow, Factor spaces of solvable groups, Ann. of Math. (2) 60 (1954), 1–27. MR 61611, DOI 10.2307/1969700
- G. D. Mostow, Fully reducible subgroups of algebraic groups, Amer. J. Math. 78 (1956), 200–221. MR 92928, DOI 10.2307/2372490
- G. D. Mostow, Representative functions on discrete groups and solvable arithmetic subgroups, Amer. J. Math. 92 (1970), 1–32. MR 271267, DOI 10.2307/2373495
- G. D. Mostow, Some applications of representative functions to solvmanifolds, Amer. J. Math. 93 (1971), 11–32. MR 283819, DOI 10.2307/2373444
- G. D. Mostow, Arithmetic subgroups of groups with radical, Ann. of Math. (2) 93 (1971), 409–438. MR 289713, DOI 10.2307/1970882
- G. D. Mostow, On the fundamental group of a homogeneous space, Ann. of Math. (2) 66 (1957), 249–255. MR 88675, DOI 10.2307/1969997
- G. D. Mostow, On maximal subgroups of real Lie groups, Ann. of Math. (2) 74 (1961), 503–517. MR 142687, DOI 10.2307/1970295
- G. D. Mostow, Homogeneous spaces with finite invariant measure, Ann. of Math. (2) 75 (1962), 17–37. MR 145007, DOI 10.2307/1970416
- G. D. Mostow, The rigidity of locally symmetric spaces, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 187–197. MR 0419683
- Masahiko Saito, Sur certains groupes de Lie résolubles, Sci. Papers College Gen. Ed. Univ. Tokyo 7 (1957), 1–11 (French). MR 97462
- John Scheuneman, Two-step nilpotent Lie algebras, J. Algebra 7 (1967), 152–159. MR 217134, DOI 10.1016/0021-8693(67)90052-X
- Richard Tolimieri, Structure of solvable Lie groups, J. Algebra 16 (1970), 597–625. MR 294564, DOI 10.1016/0021-8693(70)90010-4
- Richard Tolimieri, Applications of the semisimple splitting, Bull. Amer. Math. Soc. 77 (1971), 275–280. MR 272942, DOI 10.1090/S0002-9904-1971-12718-0
- Richard Tolimieri, On the Selberg condition for subgroups of solvable Lie groups, Bull. Amer. Math. Soc. 77 (1971), 584–586. MR 291355, DOI 10.1090/S0002-9904-1971-12762-3
- Richard Tolimieri, Homogeneous space with finite invariant measure, Geometriae Dedicata 1 (1972), no. 1, 1–5. MR 315051, DOI 10.1007/BF00147375 5. R. Tolimieri, Notes on nilpotent groups (unpublished).
- Hsien-Chung Wang, Discrete subgroups of solvable Lie groups. I, Ann. of Math. (2) 64 (1956), 1–19. MR 78645, DOI 10.2307/1969948
Additional Information
- Journal: Bull. Amer. Math. Soc. 79 (1973), 227-261
- MSC (1970): Primary 22E25
- DOI: https://doi.org/10.1090/S0002-9904-1973-13134-9
- MathSciNet review: 0486307