Identification of monoparametric families of a remarkable complex Bol algebras class, generated by the symmetric space g2/so(4)
Résumé
Our paper focuses on identification and classification of remarkable Bol algebras class generated by exceptional compact symmetric pair g2/so(4) and characterized by the identity (x.y).(z.u)=0. This study is based on a matrix realization of g2 as an algebra of anti-symmetric matrixes of order 8×8. These matrixes verify a system of invariant identities imposed by isomorphism that exists between g2 and the octonions derivations algebra. The aim of the research and its results are a part of a common classic investigation approach that specifically targets classification of mathematical studied objects . In the treated case of couple g2/so(4), our work focuses on Bol Algebras that represent the linear infinitesimal analog of local analytic (left) Bol loops generated by the homogeneous space G2/SO(4) that is symmetric, compact and of rank 2. The paper contains a complete list of the monoparametric mentioned algebras families that appear as complex solutions of a constructed matrix equations system.
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