We provide a simple coordinatization for the group G2, which is analogous to the Euler coordinatization 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. © 2005 American Institute of Physics.
Cacciatori, S., Cerchiai, B., DELLA VEDOVA, A., Ortenzi, G., Scotti, A. (2005). Euler angles for G 2. JOURNAL OF MATHEMATICAL PHYSICS, 46(8) [10.1063/1.1993549].
Euler angles for G 2
DELLA VEDOVA, ALBERTO;ORTENZI, GIOVANNI;
2005
Abstract
We provide a simple coordinatization for the group G2, which is analogous to the Euler coordinatization 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. © 2005 American Institute of Physics.
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