DOI QR코드

DOI QR Code

AUTOMORPHISMS OF UNIFORM LATTICES OF NILPOTENT LIE GROUPS UP TO DIMENSION FOUR

  • 투고 : 2019.06.03
  • 심사 : 2019.09.26
  • 발행 : 2020.04.30

초록

In this paper, when G is a connected and simply connected nilpotent Lie group of dimension less than or equal to four, we study the uniform lattices Γ of G up to isomorphism and then we study the structure of the automorphism group Aut(Γ) of Γ from the viewpoint of splitting as a natural extension.

키워드

참고문헌

  1. K. Dekimpe, Almost-Bieberbach groups: affine and polynomial structures, Lecture Notes in Mathematics, 1639, Springer-Verlag, Berlin, 1996. https://doi.org/10.1007/BFb0094472
  2. K. Y. Ha and J. B. Lee, Left invariant metrics and curvatures on simply connected three-dimensional Lie groups, Math. Nachr. 282 (2009), no. 6, 868-898. https://doi.org/10.1002/mana.200610777
  3. P. J. Kahn, Automorphisms of the discrete Heisenberg groups, preprint.
  4. J. B. Lee, K. B. Lee, J. Shin, and S. Yi, Unimodular groups of type ${\mathbb{R}}^3{\rtimes}{\mathbb{R}}$, J. Korean Math. Soc. 44 (2007), no. 5, 1121-1137. https://doi.org/10.4134/JKMS.2007.44.5.1121
  5. D. V. Osipov, The discrete Heisenberg group and its automorphism group, Math. Notes 98 (2015), no. 1-2, 185-188; translated from Mat. Zametki 98 (2015), no. 1, 152-155. https://doi.org/10.4213/mzm10694
  6. S. V. Thuong, Metrics on 4-dimensional unimodular Lie groups, Ann. Global Anal. Geom. 51 (2017), no. 2, 109-128. https://doi.org/10.1007/s10455-016-9527-z
  7. S. V. Thuong, Classification of closed manifolds with $Sol_1{^4}$-geometry, Geom. Dedicata 199 (2019), 373-397. https://doi.org/10.1007/s10711-018-0354-1