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Euler angles for G2

  • Author(s): Cacciatori, Sergio
  • Cerchiai, Bianca Letizia
  • della Vedova, Alberto
  • Ortenzi, Giovanni
  • Scotti, Antonio
  • et al.
Abstract

We provide a simple parametrization for the group G2, which is analogous to the Euler parametrization for SU(2). We show how to obtain the general element of the group in a form emphasizing the structure of the fibration of G2 with fiber SO(4) and base H, the variety of quaternionic subalgebras of octonions. In particular this allows us to obtain a simple expression for the Haar measure on G2. Moreover, as a by-product it yields a concrete realization and an Einstein metric for H.

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