SMS scnews item created by Andrew Mathas at Wed 11 Apr 2012 1457
Type: Seminar
Modified: Wed 11 Apr 2012 1500; Wed 11 Apr 2012 1501
Distribution: World
Expiry: 20 Apr 2012
Calendar1: 20 Apr 2012 1400-1500
CalLoc1: AGR Carslaw 829
CalTitle1: A tale of two G_2
Auth: mathas@pmathas.pc (assumed)

# A tale of two $$G_2$$

### Prof Boris Kruglikov

Host Venue:La Trobe University

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 $$ú^5$$. 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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