Why is split algebraic group quasi-split?
$begingroup$
One says a connected linear algebraic group $G$ over a field $k$ is quasi-split over $k$ if there exists a Borel subgroup defined over $k$, and is split if there exists a split maximal torus $T$ over $k$.
From those definitions, why is a split algebraic group quasi-split?
algebraic-geometry algebraic-groups
asked Dec 19 '18 at 18:34
zzyzzy
2,6111420
$endgroup$
add a comment |
$begingroup$
One says a connected linear algebraic group $G$ over a field $k$ is quasi-split over $k$ if there exists a Borel subgroup defined over $k$, and is split if there exists a split maximal torus $T$ over $k$.
From those definitions, why is a split algebraic group quasi-split?
algebraic-geometry algebraic-groups
asked Dec 19 '18 at 18:34
zzyzzy
2,6111420
$endgroup$
$begingroup$
@KReiser Thank you, but I mean how split implies quasi-split.
$endgroup$
– zzy
Dec 21 '18 at 3:22
add a comment |
$begingroup$
One says a connected linear algebraic group $G$ over a field $k$ is quasi-split over $k$ if there exists a Borel subgroup defined over $k$, and is split if there exists a split maximal torus $T$ over $k$.
From those definitions, why is a split algebraic group quasi-split?
algebraic-geometry algebraic-groups
asked Dec 19 '18 at 18:34
zzyzzy
2,6111420
$endgroup$
One says a connected linear algebraic group $G$ over a field $k$ is quasi-split over $k$ if there exists a Borel subgroup defined over $k$, and is split if there exists a split maximal torus $T$ over $k$.
From those definitions, why is a split algebraic group quasi-split?
algebraic-geometry algebraic-groups
algebraic-geometry algebraic-groups
asked Dec 19 '18 at 18:34
zzyzzy
2,6111420
asked Dec 19 '18 at 18:34
zzyzzy
2,6111420
asked Dec 19 '18 at 18:34
zzyzzy
2,6111420
asked Dec 19 '18 at 18:34
zzyzzy
2,6111420
asked Dec 19 '18 at 18:34
zzyzzy
2,6111420
2,6111420
$begingroup$
@KReiser Thank you, but I mean how split implies quasi-split.
$endgroup$
– zzy
Dec 21 '18 at 3:22
add a comment |
$begingroup$
@KReiser Thank you, but I mean how split implies quasi-split.
$endgroup$
– zzy
Dec 21 '18 at 3:22
$begingroup$
@KReiser Thank you, but I mean how split implies quasi-split.
$endgroup$
– zzy
Dec 21 '18 at 3:22
$begingroup$
@KReiser Thank you, but I mean how split implies quasi-split.
$endgroup$
– zzy
Dec 21 '18 at 3:22
add a comment |
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$begingroup$
@KReiser Thank you, but I mean how split implies quasi-split.
$endgroup$
– zzy
Dec 21 '18 at 3:22