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On some cohomological properties of the Lie algebra of Euclidean motions. (English) Zbl 1212.70005
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.
MSC:
70B15 Kinematics of mechanisms and robots
22E60 Lie algebras of Lie groups
22E70 Applications of Lie groups to the sciences; explicit representations
70G65 Symmetries, Lie group and Lie algebra methods for problems in mechanics
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