Euler angles for G2

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...

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Bibliographic Details
Published in:Journal of mathematical physics 2005-08, Vol.46 (8), p.083512.1-083512.17
Main Authors: CACCIATORI, Sergio L, CERCHIAI, Bianca L, DELLA VEDOVA, Alberto, ORTENZI, Giovanni, SCOTTI, Antonio
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical methods in physics
Mathematics
Physics
Sciences and techniques of general use
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Summary: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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1993549