On some cohomological properties of the Lie algebra of Euclidean motions. (English) Zbl 1212.70005

Bakšová, Marta; Dekrét, Anton

Math. Bohem. 134, No. 4, 337-348 (2009).

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