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An exposition of the structure of solvmanifolds. Part I: Algebraic theory


Author: Louis Auslander
Journal: Bull. Amer. Math. Soc. 79 (1973), 227-261
MSC (1970): Primary 22E25
DOI: https://doi.org/10.1090/S0002-9904-1973-13134-9
Part II: Bull. Amer. Math. Soc., Volume 79, Number 2 (1973), 262--285
MathSciNet review: 0486307
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  • 1. L. Auslander, On radicals of discrete subgroups of Lie groups, Amer. J. Math. 85(1963), 145-150. MR 27 #2583. MR 152607
  • 2. L. Auslander, Bieberbach's theorem on space groups and discrete uniform subgroups of Lie groups. II, Amer. J. Math. 83 (1961), 276-280. MR 23 #A962. MR 123637
  • 3. L. Auslander, Solvable Lie groups acting on nilmanifolds, Amer. J. Math. 82 (1960), 653-660. MR 23 #A241. MR 122909
  • 4. L. Auslander and L. W. Green, G-induced flows, Amer. J. Math. 88 (1966), 43-60. MR 33 #7456. MR 199308
  • 5. L. Auslander and J. Brezin, Almost algebraic Lie algebras, J. Algebra 8 (1968), 295-313. MR 37 #344. MR 224745
  • 6. L. Auslander, Fundamental groups of compact solvmanifolds, Amer. J. Math. 82 (1960), 689-697. MR 23 #A242. MR 122910
  • 7. L. Auslander, On a problem of Philip Hall, Ann. of Math. (2) 86 (1967), 112-116. MR 36 #1540. MR 218454
  • 8. L. Auslander and R. Tolimieri, Splitting theorems and the structure of solvmanifolds, Ann. of Math. (2) 92 (1970), 164-173. MR 43 #2733. MR 276995
  • 9. L. Auslander, An account of the theory of crystallographic groups, Proc. Amer. Math. Soc. 16 (1965), 1230-1236. MR 32 #2482. MR 185012
  • 10. L. Auslander, Discrete uniform subgroups of solvable Lie groups, Trans. Amer. Math. Soc. 99 (1961), 398-402. MR 24 #A1340. MR 131490
  • 11. L. Auslander, A characterization of discrete solvable matrix groups, Bull. Amer. Math. Soc. 67 (1961), 235-236. MR 23 #A945. MR 123620
  • 12. L. Auslander and M. Auslander, Solvable Lie groups and locally euclidean Riemann spaces, Proc. Amer. Math. Soc. 9 (1958), 933-941. MR 21 #2021. MR 103240
  • 13. 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 40 #8077. MR 254870
  • 14. L. Auslander, The automorphism group of a polycyclic group, Ann. of Math. (2) 89 (1969), 314-322. MR 42 #6085. MR 271202
  • 15. L. Auslander, On a problem of Philip Hall (unpublished notes).
  • 16. L. Auslander, Some compact solvmanifolds and locally affine spaces, J. Math. Mech. 7 (1958), 963-975. MR 21 #93. MR 101280
  • 17. Garrett Birkhoff, Representability of Lie algebras and Lie groups by matrices, Ann. of Math. (2) 38 (1937), no. 2, 526–532. MR 1503351, https://doi.org/10.2307/1968569
  • 1. A. I. Mal'cev, On a class of homogeneous spaces, Izv. Akad. Nauk SSSR Ser. Mat. 13 (1949), 9-22; English transl., Amer. Math. Soc. Transl. (1) 9 (1962), 276-307. MR 10, 507. MR 28842
  • 2. A. I. Mal'cev, Solvable Lie algebras, Izv. Akad. Nauk SSSR Ser. Mat. 9 (1945), 329-352; English transl., Amer. Math. Soc. Transl. (1) 9 (1962), 228-262. MR 9, 173. MR 37292
  • 3. A. I. Mal'cev, On certain classes of infinite solvable groups, Mat. Sb. 28 (70) (1951), 567-588; English transl., Amer. Math. Soc. Transl. (2) 2 (1956), 1-21. MR 12, 203; MR 17, 824. MR 43088
    C. C. Moore, Decomposition of unitary representations defined by discrete subgroups of nilpotent groups, Ann. of Math. (2) 82 (1965), 146-182. MR 31 #5928. MR 181701

  • 1. G. D. Mostow, Factor spaces of solvable groups, Ann. of Math. (2) 60 (1954), 1-27. MR 15, 853. MR 61611
  • 2. G. D. Mostow, Fully reducible subgroups of algebraic groups, Amer. J. Math. 78 (1956), 200-201. MR 19, 1181. MR 92928
  • 3. G. D. Mostow, Representative functions on discrete groups and solvable arithmetic subgroups, Amer. J. Math. 92 (1970), 1-32. MR 42 #6150. MR 271267
  • 4. G. D. Mostow, Some applications of representative functions to solvmanifolds, Amer. J. Math. 93 (1971), 11-32. MR 283819
  • 5. G. D. Mostow, Arithmetic subgroups of groups with radical, Ann. of Math. (2) 93 (1971), 409-438. MR 289713
  • 6. G. D. Mostow, On the fundamental group of a homogeneous space, Ann. of Math. (2) 66 (1957), 249-255; Errata, 590. MR 19, 561; 752. MR 88675
  • 7. G. D. Mostow, On maximal subgroups of real Lie groups, Ann. of Math. (2) 74 (1961), 503-517. MR 26 #256. MR 142687
  • 8. G. D. Mostow, Homogeneous spaces with finite invariant measure, Ann. of Math. (2) 75 (1962), 17-37. MR 26 #2546. MR 145007
  • 9. G. D. Mostow, The rigidity of locally symmetric spaces, Actes Congrès Intern. Math., 1970, tome 2, pp. 187-197. MR 419683
    M. Saito, Sur certains groupes de Lie résolubles, Sci. Papers Coll. Gen. Ed. Univ. Tokyo 7 (1957), 1-11, 157-168. MR 20 #3931; #3932. MR 97462

    J. Scheuneman, Two-step nilpotent Lie algebras, J. Algebra 7 (1967), 152-159. MR 36 #225. MR 217134

  • 1. R. Tolimieri, Structure of solvable Lie algebras, J. Algebra 16 (1970), 597-625. MR 294564
  • 2. R. Tolimieri, Applications of the semi-simple splitting, Bull. Amer. Math. Soc. 77 (1971), 275-280. MR 42 #7823. MR 272942
  • 3. R. Tolimieri, On the Selberg condition for subgroups of a solvable Lie group, Bull. Amer. Math. Soc. 77 (1971), 584-586. MR 291355
  • 4. R. Tolimieri, Finite invariant measure, Geometriae Dedicata 1 (1972). MR 315051
  • 5. R. Tolimieri, Notes on nilpotent groups (unpublished).
    H. C. Wang, Discrete subgroups of solvable Lie groups. I, Ann. of Math. (2) 64 (1956), 1-19. MR 17, 1224. MR 78645


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DOI: https://doi.org/10.1090/S0002-9904-1973-13134-9

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