• Speaker: Prof Boris Kruglikov, Department of Mathematics and Statistics, Tromsø University
  • Title: A tale of two $G_2$
  • Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Access Grid Venue: LTU [ENQUIRIES]
  • Time and Date: 2:00 pm, Fri, 20th Apr 2012
  • Abstract:

    Exceptional Lie group $G_2$ is a beautiful 14-dimensional continuous group, having relations with such diverse notions as triality, 7-dimensional cross product and exceptional holonomy. It was found abstractly by Killing in 1887 (complex case) and then realized as a symmetry group by Engel and Cartan in 1894 (real split case). Later in 1910 Cartan returned to the topic and realized split $G_2$ as the maximal finite-dimensional symmetry algebra of a rank 2 distribution in $\mathbb{R}^5$. In other words, Cartan classified all symmetry groups of Monge equations of the form $y'=f(x,y,z,z',z'')$. I will discuss the higher-dimensional generalization of this fact, based on the joint work with Ian Anderson. Compact real form of $G_2$ was realized by Cartan as the automorphism group of octonions in 1914. In the talk I will also explain how to realize this $G_2$ as the maximal symmetry group of a geometric object.

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