A tale of two G_2

Host Institution:

La Trobe University

Title of Seminar:

A tale of two G2

Speaker's Name:

Prof Boris Kruglikov

Speaker's Institution:

Tromsø University, Norway

Time and Date:

Friday 22 April 2012, 2:00pm (AEST)

Seminar Abstract:

Exceptional Lie group G2 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 G2 as the maximal finite-dimensional symmetry algebra of a rank 2 distribution in ú5. 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 G2 was realized by Cartan as the automorphism group of octonions in 1914. In the talk I will also explain how to realize this G2 as the maximal symmetry group of a geometric object.

Seminar Convenor:

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