×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite