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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
##### Keywords:
Lie group; Lie algebra; dual space; twist; wrench; cohomology
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