What is the Lie algebra of the euclidean group?
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The Lie algebra of the Euclidean group, denoted as se(3), is the algebra of the infinitesimal elements of the Euclidean group SE(3) . It is isomorphic to the motor algebra of von Mises and the theory of screws of Ball . The Lie algebra se(3) can elegantly model the infinitesimal kinematics of the rigid body, including velocity, acceleration, jerk, and more, especially in open and closed kinematic chains . The Lie algebra se(3) is also considered as a vector space matrix of the angular velocity vectors . It is an abelian extension of the orthogonal Lie algebra and its Leibniz (co)homology can be computed via the identification of certain orthogonal invariants .
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01 Jan 2022 | The Lie algebra of the Euclidean group SE(3) is se(3). |
| The provided paper does not mention the Lie algebra of the Euclidean group. |
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