Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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QUATERNIONIC HEISENBERG GROUP

  • Shin, Joonkook (Department of Mathematics Chungnam National University) ;
  • Hong, Sungsook (Department of Mathematics Chungnam National University)
  • Received : 2003.06.24
  • Published : 2003.06.30
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Abstract

We shall study the automorphism group of the quaternionic Heisenberg group $\mathcal{H}_7(\mathbb{H})=\mathbb{R}^3{\tilde{\times}}\mathbb{H}$ which is important to investigate an almost Bieberbach group of a 7-dimensinal infra-nilmanifold and show that Aut$$(\mathbb{R}^3{\tilde{\times}}\mathbb{R}^4){\sim_=}Hom(\mathbb{R}^4,\mathbb{R}^3){\rtimes}O(J;2,2)$$.

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