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[Merged by Bors] - refactor(representation_theory/group_cohomology_resolution): refactor k[G^{n + 1}]
isomorphism
#18271
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k[G^{n + 1}]
isomorphismk[G^{n + 1}]
isomorphism
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Thanks! This looks fine to me -- I've left some comments. I managed to golf two proofs (reducing two inductions to one) and this is probably worth including if you can't see any disadvantages with my potential definition change.
@101damnations, could you resolve the conflicts? Feel free to ping me afterwards, I'd like to get this in! |
@semorrison Thank you, I've sorted the conflicts |
Is this meant to be labelled |
bors merge |
… `k[G^{n + 1}]` isomorphism (#18271) This refactors the isomorphism $k[G^{n + 1}] \cong k[G] \otimes_k k[G^n]$ (where $G$ acts by left multiplication on $k[G^{n + 1}]$ and $k[G]$ but trivially on $k[G^n]$) to use an isomorphism of $G$-sets $G^{n + 1} \cong G \times G^n.$
Pull request successfully merged into master. Build succeeded: |
k[G^{n + 1}]
isomorphismk[G^{n + 1}]
isomorphism
This refactors the isomorphism$k[G^{n + 1}] \cong k[G] \otimes_k k[G^n]$ (where $G$ acts by left multiplication on $k[G^{n + 1}]$ and $k[G]$ but trivially on $k[G^n]$ ) to use an isomorphism of $G$ -sets $G^{n + 1} \cong G \times G^n.$
This PR doesn't really need to exist but I got carried away.
I generalised the definition of
representation.trivial
, but can undo this if necessary.