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Geometric oduli. (Russian) Zbl 0637.53014
Webs and quasigroups, Interuniv. thematic Collect. sci. Works, Kalinin 1987, 88-98 (1987).
[For the entire collection see Zbl 0611.00007.]
The subject of this paper is devoted to further investigation of the relations between the objects of nonassociative algebra and differential geometry. [For a detailed interpretation of these ideas and some main results see the fundamental work of the author [Methods of nonassociative algebra in differential geometry. Addition to S. Kobayashi and K. Nomizu, Foundations of differential geometry V. II. (Russian) (Nauka, Moskva 1981; Zbl 0526.53001)].
An odule \(<M,\cdot,\epsilon,(t)_{t\in {\mathbb{R}}}>\) is called geometric if the following identity holds: \(\ell (a,y)ty=t\ell (a,y)y\) where \(\ell (a,y)={\mathcal L}^{-1}_{ay}\cdot {\mathcal L}_ a\cdot {\mathcal L}_ y\). The paper contains a proof of the following statement: any geometric odule can be realized as a geodesic odule for some space with an affine connection.
Reviewer: M.Malakhal’tsev

53B05 Linear and affine connections
17D99 Other nonassociative rings and algebras
53C05 Connections (general theory)