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Weight spaces of Malt’sev modules. (Espaces poids des modules de Malcev.) (French. English summary) Zbl 1172.17023
Consider a finite dimensional Mal’tsev algebra $$M$$ of a field $$k$$ of characteristic zero, and a finite dimensional module $$V$$ for $$M$$ associated with a representation $$\rho$$. For is a linear functional $$\lambda$$ on $$M$$ denote by $$V^{\lambda}$$ the union of kernels of operators $$\left(\rho_x -\lambda(x)\right)^n,\; n\geqslant 1,$$ in $$V$$. There are found criterions under which $$V^{\lambda}$$ is a nonzero submodule in $$V$$. For example it means that $$\lambda$$ is a character of $$M$$. An analog of of theorem of Lie is proved for solvable Mal’tsev algebras.
##### MSC:
 17D10 Mal’tsev rings and algebras
##### Keywords:
Mal’tsev algebras; representations