projective group

projective group

[prə′jek·tiv ′grüp]
(mathematics)
A group of transformations arising in the general theory of projective geometry.
References in periodicals archive ?
In particular, if g [equivalent to] Id and if the [s.sub.i] are fixed, then the set of localized events x [equivalent to] [e.sub.AL] [member of] [R.sup.4.sub.AL] is an orbit of GL(4, R) and the set of corresponding events [e.sub.P] = [pi]([e.sub.AL]) is an orbit of the projective group PGL(4, R).
In other words, the equivariance is defined for Euclidean tensors with respect to linear groups of transformations whereas the equivariance for projective tensors is defined with respect to the group of central collineations which is a subgroup of the projective group.
These humoristic references to a uniting nerd culture channel a projective group identity of otherness.
As an application, we show that the identities proved by De Medts and Segev [2] for the so-called [micro]-operators in the little projective group of a Moufang set hold in fact in an arbitrary rank one group.
The little projective group of M is G(M) = (U(p) : p [member of] X) [subset] Sym(X).
Let M = (X, U) be a Moufang set with basis b, let [U.sup.[sigma]]= U ([b.sup.[sigma]]) and let [??] = G(M) be the little projective group of M.
Let [bar.G] be the little projective group of M and put [[bar.U].sup.[sigma]]= U ([b.sup.[sigma]]) as in Lemma 3.3.
This is not the case because the little projective group of a Moufang set M does not depend functorially on M.
In this section we generalize these results to all projective groups of type G(r, p, s, n).