An isomorphism of modules and an action of a Galois group
$begingroup$
Let $K subset L$ be a finite Galois extension and $text{Gal}(L/K) = G$. Suppose we have a vector space $V$ over $L$ and an isomorphism $alpha: V otimes_K L to V otimes_K L$ between $L otimes_K L-$modules. Is there any canonical way to define a such $K-$linear action of $G$ on $V$ that for all $g in G, l in L, v in V$ holds $g(lv) = g(l) g(v)$?
modules group-actions galois-extensions
asked Dec 15 '18 at 4:40
iouiou
5617
$endgroup$
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$begingroup$
Let $K subset L$ be a finite Galois extension and $text{Gal}(L/K) = G$. Suppose we have a vector space $V$ over $L$ and an isomorphism $alpha: V otimes_K L to V otimes_K L$ between $L otimes_K L-$modules. Is there any canonical way to define a such $K-$linear action of $G$ on $V$ that for all $g in G, l in L, v in V$ holds $g(lv) = g(l) g(v)$?
modules group-actions galois-extensions
asked Dec 15 '18 at 4:40
iouiou
5617
$endgroup$
add a comment |
$begingroup$
Let $K subset L$ be a finite Galois extension and $text{Gal}(L/K) = G$. Suppose we have a vector space $V$ over $L$ and an isomorphism $alpha: V otimes_K L to V otimes_K L$ between $L otimes_K L-$modules. Is there any canonical way to define a such $K-$linear action of $G$ on $V$ that for all $g in G, l in L, v in V$ holds $g(lv) = g(l) g(v)$?
modules group-actions galois-extensions
asked Dec 15 '18 at 4:40
iouiou
5617
$endgroup$
Let $K subset L$ be a finite Galois extension and $text{Gal}(L/K) = G$. Suppose we have a vector space $V$ over $L$ and an isomorphism $alpha: V otimes_K L to V otimes_K L$ between $L otimes_K L-$modules. Is there any canonical way to define a such $K-$linear action of $G$ on $V$ that for all $g in G, l in L, v in V$ holds $g(lv) = g(l) g(v)$?
modules group-actions galois-extensions
modules group-actions galois-extensions
asked Dec 15 '18 at 4:40
iouiou
5617
asked Dec 15 '18 at 4:40
iouiou
5617
asked Dec 15 '18 at 4:40
iouiou
5617
asked Dec 15 '18 at 4:40
iouiou
5617
asked Dec 15 '18 at 4:40
iouiou
5617
5617
add a comment |
add a comment |
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