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Geodesic multiplication and the theory of gravity. (English) Zbl 0806.53085
Summary: Nonassociative algebraic systems called local geodesic loops and their tangent Akivis algebras are considered. The construction of geo-odular structure of a manifold with an affine connection is briefly reviewed. A possible role of these algebraic structures in classical and quantum gravity is discussed.

53Z05 Applications of differential geometry to physics
83E30 String and superstring theories in gravitational theory
Full Text: DOI
[1] Sabinin L. V., Dokl. Akad. Nauk SSSR 233 pp 800– (1977)
[2] Sabinin L. V., Trans. Inst. Phys. Estonian Acad. Sci. 66 pp 24– (1990)
[3] Akivis M. A., Sibirski Mat. J. 19 pp 243– (1978) · Zbl 0409.53008 · doi:10.1007/BF00970497
[4] Kikkawa M., Hiroshima J. Univ. Ser. A-l. Math. 28 pp 199– (1964)
[5] DOI: 10.1090/S0002-9947-1943-0009962-7 · doi:10.1090/S0002-9947-1943-0009962-7
[6] Mal’tsev A., Mat. Sb. 36 pp 569– (1955)
[7] DOI: 10.4153/CJM-1965-056-8 · Zbl 0138.25601 · doi:10.4153/CJM-1965-056-8
[8] Akivis M. A., Sibirski Mat. J. 17 pp 5– (1976) · Zbl 0337.53018 · doi:10.1007/BF00969285
[9] DOI: 10.1007/BF00759173 · Zbl 0362.53013 · doi:10.1007/BF00759173
[10] Alexandrov A. N., Teor. Mat. Fiz. 38 pp 71– (1979)
[11] Kuusk P., Trans. Tallinn Techn. Univ. 733 pp 33– (1992)
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