This article is cited in 9 papers

The groups of motions of some three-dimensional maximal mobility geometries

V. A. Kyrov, R. A. Bogdanova

Gorno-Altaisk State University, Gorno-Altaisk, Russia

Abstract: We find the groups of motions of eight three-dimensional maximal mobility geometries. These groups are actions of just three Lie groups $SL_2(R)\triangleright N$, $SL_2(C)_R$, and $SL_2(R)\otimes SL_2(R)$ on the space $R^3$, where $N$ is a normal abelian subgroup. We also find explicit expressions for these actions.

Keywords: maximal mobility geometry, group of motions, Lie group, Lie algebra.

UDC: 512.816

MSC: 35R30

Received: 11.07.2017

DOI: 10.17377/smzh.2018.59.215

 English version: Siberian Mathematical Journal, 2018, 59:2, 323–331

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