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Results tagged with projective-geometry
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user 12858
6
votes
Synthetic projective lines
Following up on Matthias Wendt's comment, the language of Moufang sets is indeed a suitable axiomatic approach to (generalizations of) projective lines.
Formally speaking, a Moufang set is a set $X$ …
- 6,614
9
votes
2
answers
441
views
Embedding $\mathrm{PGL}(n,q^h)$ in $\mathrm{PGL}(nh,q)$
It is not very hard to see that for each prime power $q$ and natural numbers $n,h$, we have an embedding
$$\iota \colon \mathrm{GL}(n,q^h) \hookrightarrow \mathrm{GL}(nh, q),$$
obtained by choosing a …
- 6,614
3
votes
Moufang identities and Moufang plane
A very accessible book for such connections between geometric and algebraic properties in general, is John Faulkner's "The Role of Nonassociative Algebra in Projective Geometry" (https://bookstore.ams …
- 6,614
10
votes
Accepted
Which finite projective planes can have a symmetric incidence matrix?
The key word here is "polarity". A polarity of a projective plane with point set $P$ and line set $L$ is a map $\pi$ from $P \cup L$ to itself mapping points to lines and lines to points, such that $\ …
- 6,614