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On holonomy representations of manifolds modelled on modules over Weil algebra

L. В. Smolyakova

Kazan State University

Abstract: In [5], [6], for the canonical foliations of manifolds over local algebra $\mathbf A$ determined by ideals of $\mathbf A$, V. V. Shurygin defined and studied holonomy leaf representations. In the present paper we define holonomy representations for manifolds modelled on an $\mathbf A$-module $\mathbf L=\mathbf A^n\oplus\mathbf B^m$, where $\mathbf B$ is a quotient algebra of $\mathbf A$, and find interrelation of these representations with the holonomy representations defined in the foliation theory [3], [4] and in the theory of $(X,G)$-manifolds [1].