Communications of the
Korean Mathematical Society CKMS

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Commun. Korean Math. Soc. 2020; 35(2): 653-666

Online first article January 29, 2020      Printed April 30, 2020

https://doi.org/10.4134/CKMS.c190192

Copyright © The Korean Mathematical Society.

Automorphisms of uniform lattices of nilpotent Lie groups up to dimension four

Jong Bum Lee, Sang Rae Lee

Sogang University; Texas A\&M University

Abstract

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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 $\Gamma$ of $G$ up to isomorphism and then we study the structure of the automorphism group $\aut(\Gamma)$ of $\Gamma$ from the viewpoint of splitting as a natural extension.

Keywords: Automorphism, nilpotent Lie group, splitting, uniform lattice

MSC numbers: Primary 22E25; Secondary 22E40

Supported by: The first-named author is supported in part by Basic Science Research Program through
the National Research Foundation of Korea(NRF) funded by the Ministry of Education
(NRF2016R1D1A1B01006971).

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