Baklouti, Ali Deformation of discontinuous subgroups acting on some nilpotent homogeneous spaces. (English) Zbl 1198.57024 Proc. Japan Acad., Ser. A 85, No. 4, 41-45 (2009). This report on \(2n+1\)-dimensional Heisenberg groups formulates the topics in the sense of T. Kobayashi’s problem. The author promises the detailed proofs elsewhere. Reviewer: Emil Molnár (Budapest) Cited in 1 Document MSC: 57S30 Discontinuous groups of transformations 22F30 Homogeneous spaces 22E25 Nilpotent and solvable Lie groups 32G05 Deformations of complex structures Keywords:Heisenberg group; proper action; discontinuous subgroup; deformation space × Cite Format Result Cite Review PDF Full Text: DOI References: [1] A. Baklouti and I. Kédim, On the deformation space of Clifford-Klein forms of some exponential homogeneous spaces, Int. J. Math. (to appear). · Zbl 1185.22004 · doi:10.1142/S0129167X0900556X [2] A. Baklouti, I. Kédim and T. Yoshino, On the deformation space of Clifford-Klein forms of Heisenberg groups, Int. Math. Res. Not. IMRN (2008), no. 16, pp. 35. · Zbl 1154.22011 [3] T. Kobayashi, Criterion for proper actions on homogeneous spaces of reductive groups, J. Lie Theory 6 (1996), no. 2, 147-163. · Zbl 0863.22010 [4] T. Kobayashi, Deformation of compact Clifford-Klein forms of indefinite-Riemannian homogeneous manifolds, Math. Ann. 310 (1998), no. 3, 395-409. · Zbl 0891.22014 · doi:10.1007/s002080050153 [5] T. Kobayashi, Discontinuous groups for non-Riemannian homogeneous spaces, in Mathematics unlimited–2001 and beyond , Springer, Berlin, 2001, pp. 723-747. · Zbl 1023.53031 · doi:10.1007/978-3-642-56478-9_8 [6] T. Kobayashi, Discontinuous groups acting on homogeneous spaces of reductive type, in Representation theory of Lie groups and Lie algebras (Fuji-Kawaguchiko, 1990) , World Sci. Publ., River Edge, NJ, 1992, pp. 59-75. · Zbl 1193.22010 [7] T. Kobayashi, On discontinuous groups acting on homogeneous spaces with noncompact isotropy subgroups, J. Geom. Phys. 12 (1993), no. 2, 133-144. · Zbl 0815.57029 · doi:10.1016/0393-0440(93)90011-3 [8] T. Kobayashi, Proper action on a homogeneous space of reductive type, Math. Ann. 285 (1989), no. 2, 249-263. · Zbl 0662.22008 · doi:10.1007/BF01443517 [9] T. Kobayashi and S. Nasrin, Deformation of properly discontinuous actions of \(\mathbf{Z}^{k}\) on \(\mathbf{R}^{k+1}\), Internat. J. Math. 17 (2006), no. 10, 1175-1193. · Zbl 1124.57015 · doi:10.1142/S0129167X06003862 [10] T. Kobayashi and T. Yoshino, Compact Clifford-Klein forms of symmetric spaces–revisited, Pure Appl. Math. Q. 1 (2005), no. 3, part 2, 591-663. · Zbl 1145.22011 · doi:10.4310/PAMQ.2005.v1.n3.a6 [11] R. S. Palais, On the existence of slices for actions of non-compact Lie groups, Ann. of Math. (2) 73 (1961), 295-323. · Zbl 0103.01802 · doi:10.2307/1970335 [12] A. Weil, Remarks on the cohomology of groups, Ann. of Math. (2) 80 (1964), 149-157. · Zbl 0192.12802 · doi:10.2307/1970495 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.