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Our manual entries for PGL, PSL, etc. define these as "modulo the center".
But formally, the definition is not to take the quotient modulo the center, but rather modulo scalar matrices (achieved implicitly by using a projective action on the vector). The two are related by not completely trivial mathematics. I think this can be confusing to users and perhaps also result in some other misconceptions.
Anyway, I guess what I am saying is that it might be better if we described in a separate section / paragraph what we mean by projective group (modulo scalars, equiv: acting on lines) and that this means we take a central factor, and that for many important cases ("full" groups) this in fact means factoring out the whole center. And then we can just reference that.
Such a section on projective actions would be useful. It could refer to the FinInG package. (I had expected that also the recog package contains something interesting in this respect, but I did not find this at first sight.) In the other direction, the functions NormedVectors, OnLines, ProjectiveActionOnFullSpace, ProjectiveOrder could refer to the new section.
The text was updated successfully, but these errors were encountered:
Our manual entries for PGL, PSL, etc. define these as "modulo the center".
But formally, the definition is not to take the quotient modulo the center, but rather modulo scalar matrices (achieved implicitly by using a projective action on the vector). The two are related by not completely trivial mathematics. I think this can be confusing to users and perhaps also result in some other misconceptions.
Anyway, I guess what I am saying is that it might be better if we described in a separate section / paragraph what we mean by projective group (modulo scalars, equiv: acting on lines) and that this means we take a central factor, and that for many important cases ("full" groups) this in fact means factoring out the whole center. And then we can just reference that.
Originally posted by @fingolfin in #4334 (comment)
@ThomasBreuer added:
Such a section on projective actions would be useful. It could refer to the FinInG package. (I had expected that also the recog package contains something interesting in this respect, but I did not find this at first sight.) In the other direction, the functions
NormedVectors
,OnLines
,ProjectiveActionOnFullSpace
,ProjectiveOrder
could refer to the new section.The text was updated successfully, but these errors were encountered: