使成核 发表于 2025-3-28 17:16:38
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Infinitesimal Theory of Smooth Loopsoriginal approach used by S. Lie for Lie groups (with modifications), since, in order to understand the principal notions, one has to return to origins on the basis of differential equations. the differential equations of smooth loops are introduced and their infinitesimal theory is constructed genearrogant 发表于 2025-3-29 02:52:14
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Smooth Hyporeductive and Pseudoreductive Loopsesimal theory (similar to Lie group theory) if one associates with the loop certain binaryternary tangent algebra with identities, in the first case a Bol algebra, in the second case a triple Lie algebra. But it is possible to consider a more general case of hyporeductive loops [L.V. Sabinin 90b,c,d烦忧 发表于 2025-3-29 12:22:34
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Geometry of Smooth Bol and Moufang Loopsfold with zero curvature (with absolute parallelism). Further, the techniques of differential geometry is used to prove the main structure theorem in the theory of local analytic Bol loops. the affine connection in the question is a generalization of the Cartan connection with zero curvature on LieEnzyme 发表于 2025-3-30 05:30:02
Smooth Hyporeductive and Pseudoreductive Loopsome linear algebra equipped with two binary and one ternary operations and the system of identities (so called .). Such an algebra is the generalization of Bol algebra and triple Lie algebra, both. In this Chapter we shall construct the infinitesimal theory of smooth hyporeductive and pseudoreductive loops.