Mixing
Algebraic Groups, dual numbers and differentials
$begingroup$
I was looking for a method to compute the explicit differential of a regular map between algebraic groups. More precisely if $X$ is a sub-variety in an algebraic group $G$ (say over a finite field $k$), I'd like to compute the differential of the map
begin{align}
phi:Xtimes X&longrightarrow G\
(x_1,x_2)&longmapsto (x_1*x_2),
end{align}
where * is the group low.
I found this related question, "What is the differential of a translation map on an algebraic group?" but I'm a bit confused about the re-interpretation of the tangent bundle and the dual numbers. Can someone explain me a bit more what is going on?
Thank you very much!
algebraic-groups differential tangent-bundle
asked Jan 26 at 20:03
Filippo SneakerheadFilippo Sneakerhead
285
$endgroup$
add a comment |
$begingroup$
I was looking for a method to compute the explicit differential of a regular map between algebraic groups. More precisely if $X$ is a sub-variety in an algebraic group $G$ (say over a finite field $k$), I'd like to compute the differential of the map
begin{align}
phi:Xtimes X&longrightarrow G\
(x_1,x_2)&longmapsto (x_1*x_2),
end{align}
where * is the group low.
I found this related question, "What is the differential of a translation map on an algebraic group?" but I'm a bit confused about the re-interpretation of the tangent bundle and the dual numbers. Can someone explain me a bit more what is going on?
Thank you very much!
algebraic-groups differential tangent-bundle
asked Jan 26 at 20:03
Filippo SneakerheadFilippo Sneakerhead
285
$endgroup$
add a comment |
$begingroup$
I was looking for a method to compute the explicit differential of a regular map between algebraic groups. More precisely if $X$ is a sub-variety in an algebraic group $G$ (say over a finite field $k$), I'd like to compute the differential of the map
begin{align}
phi:Xtimes X&longrightarrow G\
(x_1,x_2)&longmapsto (x_1*x_2),
end{align}
where * is the group low.
I found this related question, "What is the differential of a translation map on an algebraic group?" but I'm a bit confused about the re-interpretation of the tangent bundle and the dual numbers. Can someone explain me a bit more what is going on?
Thank you very much!
algebraic-groups differential tangent-bundle
asked Jan 26 at 20:03
Filippo SneakerheadFilippo Sneakerhead
285
$endgroup$
I was looking for a method to compute the explicit differential of a regular map between algebraic groups. More precisely if $X$ is a sub-variety in an algebraic group $G$ (say over a finite field $k$), I'd like to compute the differential of the map
begin{align}
phi:Xtimes X&longrightarrow G\
(x_1,x_2)&longmapsto (x_1*x_2),
end{align}
where * is the group low.
I found this related question, "What is the differential of a translation map on an algebraic group?" but I'm a bit confused about the re-interpretation of the tangent bundle and the dual numbers. Can someone explain me a bit more what is going on?
Thank you very much!
algebraic-groups differential tangent-bundle
algebraic-groups differential tangent-bundle
asked Jan 26 at 20:03
Filippo SneakerheadFilippo Sneakerhead
285
asked Jan 26 at 20:03
Filippo SneakerheadFilippo Sneakerhead
285
asked Jan 26 at 20:03
Filippo SneakerheadFilippo Sneakerhead
285
asked Jan 26 at 20:03
Filippo SneakerheadFilippo Sneakerhead
285
asked Jan 26 at 20:03
Filippo SneakerheadFilippo Sneakerhead
285
285
add a comment |
add a comment |
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