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On some cohomological properties of the Lie algebra of Euclidean motions

Marta Bakšová, Anton Dekrét (2009)

Mathematica Bohemica

The external derivative d on differential manifolds inspires graded operators on complexes of spaces Λ r g * , Λ r g * g , Λ r g * g * stated by g * dual to a Lie algebra g . Cohomological properties of these operators are studied in the case of the Lie algebra g = s e ( 3 ) of the Lie group of Euclidean motions.

On the equivalence of control systems on Lie groups

Rory Biggs, Claudiu C. Remsing (2015)

Communications in Mathematics

We consider state space equivalence and feedback equivalence in the context of (full-rank) left-invariant control systems on Lie groups. We prove that two systems are state space equivalent (resp.~detached feedback equivalent) if and only if there exists a Lie group isomorphism relating their parametrization maps (resp. traces). Local analogues of these results, in terms of Lie algebra isomorphisms, are also found. Three illustrative examples are provided.

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