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[Merged by Bors] - refactor(representation_theory/group_cohomology_resolution): refactor k[G^{n + 1}] isomorphism #18271

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@101damnations 101damnations commented Jan 23, 2023

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.

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@101damnations 101damnations changed the title feat(representation_theory/group_cohomology_resolution): refactor k[G^{n + 1}] isomorphism refactor(representation_theory/group_cohomology_resolution): refactor k[G^{n + 1}] isomorphism Jan 23, 2023
@101damnations 101damnations added the awaiting-review The author would like community review of the PR label Jan 24, 2023
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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.

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@semorrison semorrison added awaiting-author A reviewer has asked the author a question or requested changes merge-conflict Please `git merge origin/master` then a bot will remove this label. and removed awaiting-review The author would like community review of the PR labels Mar 28, 2023
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@101damnations, could you resolve the conflicts? Feel free to ping me afterwards, I'd like to get this in!

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@semorrison Thank you, I've sorted the conflicts

@101damnations 101damnations removed awaiting-author A reviewer has asked the author a question or requested changes merge-conflict Please `git merge origin/master` then a bot will remove this label. labels Mar 29, 2023
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Is this meant to be labelled awaiting-review? If you don't label it, it won't appear on the #queue.

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bors merge

@github-actions github-actions bot added the ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) label Mar 29, 2023
bors bot pushed a commit that referenced this pull request Mar 30, 2023
… `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 $G^{n + 1} \cong G \times G^n.$
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bors bot commented Mar 30, 2023

Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title refactor(representation_theory/group_cohomology_resolution): refactor k[G^{n + 1}] isomorphism [Merged by Bors] - refactor(representation_theory/group_cohomology_resolution): refactor k[G^{n + 1}] isomorphism Mar 30, 2023
@bors bors bot closed this Mar 30, 2023
@bors bors bot deleted the equiv_tensor_refactor branch March 30, 2023 03:40
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