等質リー・ループの標準接続と3ウェブ

A differentiable left I. P. loop (G, μ) admits on the tangent space at the unit element two kinds of bilinear operations dμ and dL which are induced from the multiplication μ and left inner mappings. In this paper, after recalling some formulas of the Chern connection of a local 3-web of a differentiable loop, relations between this connection and bilinear operation above are investigated in differentiable left I. P. loops. The results are applied to homogeneousLie loops and it is shown that the bilinear- and trilinear products of the tangent Lie triple algebras are given by the torsion and the curvature of the Chern connections.