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Euler angles for G2

Sergio L. Cacciatori·Bianca L. Cerchiai·Alberto Della Vedova·Giovanni Ortenzi·Antonio Scotti
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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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Sergio L. Cacciatori, Bianca L. Cerchiai, Alberto Della Vedova, Giovanni Ortenzi, Antonio Scotti. 2005-05-06. Euler angles for G2. https://doi.org/10.1063/1.1993549

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