On some cohomological properties of the Lie algebra of Euclidean motions

summary:The external derivative $d$ on differential manifolds inspires graded operators on complexes of spaces $\Lambda ^rg^\ast $, $\Lambda ^rg^\ast \otimes g$, $\Lambda ^rg^\ast \otimes g^\ast $ stated by $g^\ast $ dual to a Lie algebra $g$. Cohomological properties of these operators are studied in the case of the Lie algebra $g=se( 3 )$ of the Lie group of Euclidean motions