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Questions of the kind "What's the name for a X that satisfies property Y?"

6 votes
0 answers
230 views

Group homomorphism from $\mathrm{GL}_p$ to $\mathrm{SL}_p$ in characteristic $p$

If $k$ is a commutative field of characteristic $p>0$, then the map $$ \theta \colon \mathrm{GL}_p(k) \to \mathrm{SL}_p(k) \colon A = (a_{ij}) \mapsto (\det A)^{-1} (a_{ij}^p) $$ is a group homomorphi …
Tom De Medts's user avatar
  • 6,614
3 votes
0 answers
93 views

Projective limit of copies of same group w.r.t. some fixed endomorphism

In our study of automorphism groups of transcendental field extensions, we have encountered the situation where we have a group $F$ together with an endomorphism $\alpha \colon F \to F$, resulting in …
Tom De Medts's user avatar
  • 6,614
6 votes

Cayley-Dickson form of a quaternion

I believe there is a good reason why mathematicians don't use the terminology "simplex-part" and "perplex-part": they are not canonical! … (This terminology is also used for octonions, and also for (generalized) quaternion and octonion algebras over arbitrary fields of characteristic different from $2$.) …
Tom De Medts's user avatar
  • 6,614