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On a Lie group, exp is a map from the Lie algebra to its Lie group. If you think of the Lie algebra as the tangent space to the identity of the Lie group, exp(v) is defined ...

A polygon whose vertices do not all lie in a plane.

Every finite-dimensional Lie algebra of characteristic p=0 has a faithful finite-dimensional representation.

An operator Gamma=sum_(i=1)^me_i^Ru^(iR) on a representation R of a Lie algebra.

Every finite-dimensional Lie algebra of characteristic p!=0 has a faithful finite-dimensional representation.

A Lie algebra is a vector space g with a Lie bracket [X,Y], satisfying the Jacobi identity. Hence any element X gives a linear transformation given by ad(X)(Y)=[X,Y], (1) ...

The geometry of the Lie group R semidirect product with R^2, where R acts on R^2 by (t,(x,y))->(e^tx,e^(-t)y).

A conic section on which the midpoints of the sides of any complete quadrangle lie. The three diagonal points P, Q, and R also lie on this conic.

A set of points which do not lie on any of a certain class of hyperplanes.

A point which does not lie on at least one ordinary line.