Geodesic
On some cohomological properties of the Lie algebra of Euclidean motions
Mathematica Bohemica, Tome 134 (2009) no. 4, pp. 337-348

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MR Zbl
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.
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.
DOI : 10.21136/MB.2009.140665
Classification : 22E60, 22E70, 70B15
Keywords: Lie group; Lie algebra; dual space; twist; wrench; cohomology 
Bakšová, Marta; Dekrét, Anton. On some cohomological properties of the Lie algebra of Euclidean motions. Mathematica Bohemica, Tome 134 (2009) no. 4, pp. 337-348. doi: 10.21136/MB.2009.140665
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