Euler angles for G2

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.

21 pages, 2 figures, some misprints corrected

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• Exceptional Lie Algebras, SU(3) and Jordan Pairs Part 2: Zorn-type Representations
• Topology and $\theta$ dependence in finite temperature $G_2$ lattice gauge theory
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• Vacua and RG flows in N=9 three dimensional gauged supergravity
• Perturbing Around A Warped Product Of AdS_4 and Seven-Ellipsoid
• Gaugings of N=4 three dimensional gauged supergravity with exceptional coset manifolds
• Gauge-covariant decomposition and magnetic monopole for G(2) Yang-Mills field