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feat(RingTheory/HopfAlgebra): Construction on primitive elements#39841

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feat(RingTheory/HopfAlgebra): Construction on primitive elements#39841
hawkrobe wants to merge 20 commits into
leanprover-community:masterfrom
hawkrobe:coalgebra-graded-connected

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@hawkrobe

@hawkrobe hawkrobe commented May 25, 2026

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Builds a Hopf algebra structure on a bialgebra generated by primitive elements.


Please let me know if it would be better to split into multiple PRs (e.g. Bialgebra/Primitive.lean first)!

@github-actions github-actions Bot added the new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! label May 25, 2026
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Welcome new contributor!

Thank you for contributing to Mathlib! If you haven't done so already, please review our contribution guidelines, as well as the style guide and naming conventions. In particular, we kindly remind contributors that we have guidelines regarding the use of AI when making pull requests.

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@github-actions github-actions Bot added merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) t-ring-theory Ring theory and removed merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) labels May 25, 2026
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github-actions Bot commented May 25, 2026

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PR summary 58a70be302

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.RingTheory.Bialgebra.Primitive (new file) 1129
Mathlib.RingTheory.HopfAlgebra.Generators (new file) 1138
Mathlib.RingTheory.HopfAlgebra.Primitive (new file) 1140

Declarations diff (regex)

+ IsPrimitiveElem
+ IsPrimitiveElem.add
+ IsPrimitiveElem.antipode
+ IsPrimitiveElem.antipode_antipode
+ IsPrimitiveElem.antipode_eq_neg
+ IsPrimitiveElem.commutator
+ IsPrimitiveElem.map
+ IsPrimitiveElem.ne_one
+ IsPrimitiveElem.neg
+ IsPrimitiveElem.smul
+ IsPrimitiveElem.sub
+ IsPrimitiveElem.zero
+ convMul_eq_one_of_adjoin_eq_top_left
+ convMul_eq_one_of_adjoin_eq_top_right
+ eq_antipodeAlgHomOp_of_primitives
+ eq_antipode_of_adjoin_eq_top_left
+ eq_antipode_of_adjoin_eq_top_right
+ eq_antipode_of_convMul_id_eq_one
+ eq_antipode_of_id_convMul_eq_one
+ isPrimitiveElem_map_equiv
+ mem_primitiveSubmodule
+ ofGenerators
+ ofPrimitives
+ primitiveSubmodule

You can run this locally as follows
## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

Lean-aware diff — post-build, computed from the Lean environment (commit 58a70be).

  • +31 new declarations
  • −0 removed declarations
+HopfAlgebra.eq_antipodeAlgHomOp_of_primitives
+HopfAlgebra.eq_antipode_of_adjoin_eq_top_left
+HopfAlgebra.eq_antipode_of_adjoin_eq_top_right
+HopfAlgebra.eq_antipode_of_convMul_id_eq_one
+HopfAlgebra.eq_antipode_of_id_convMul_eq_one
+HopfAlgebra.ofGenerators
+HopfAlgebra.ofPrimitives
+IsPrimitiveElem
+IsPrimitiveElem.add
+IsPrimitiveElem.antipode
+IsPrimitiveElem.antipode_antipode
+IsPrimitiveElem.antipode_eq_neg
+IsPrimitiveElem.casesOn
+IsPrimitiveElem.commutator
+IsPrimitiveElem.comul_eq_tmul_add_tmul
+IsPrimitiveElem.counit_eq_zero
+IsPrimitiveElem.map
+IsPrimitiveElem.mk
+IsPrimitiveElem.ne_one
+IsPrimitiveElem.neg
+IsPrimitiveElem.rec
+IsPrimitiveElem.recOn
+IsPrimitiveElem.smul
+IsPrimitiveElem.sub
+IsPrimitiveElem.zero
+LinearMap.convMul_eq_one_of_adjoin_eq_top_left
+LinearMap.convMul_eq_one_of_adjoin_eq_top_right
+isPrimitiveElem_iff
+isPrimitiveElem_map_equiv
+mem_primitiveSubmodule
+primitiveSubmodule

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 58a70be302
Reference commit 4851ebd9bf

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@hawkrobe
hawkrobe force-pushed the coalgebra-graded-connected branch from d55e3bf to 62d838a Compare May 25, 2026 16:43
@github-actions github-actions Bot added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label May 25, 2026
@hawkrobe
hawkrobe force-pushed the coalgebra-graded-connected branch from 62d838a to 82a9475 Compare May 25, 2026 16:46
@github-actions github-actions Bot removed the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label May 25, 2026
@hawkrobe hawkrobe changed the title feat(RingTheory/HopfAlgebra): primitive-generated construction feat(RingTheory/HopfAlgebra): Construction on primitive elements May 25, 2026
@hawkrobe
hawkrobe force-pushed the coalgebra-graded-connected branch 5 times, most recently from 81cb56a to fd6aa8e Compare May 27, 2026 20:17
@hawkrobe
hawkrobe force-pushed the coalgebra-graded-connected branch 2 times, most recently from 1092b0e to b25795e Compare June 4, 2026 01:47
@hawkrobe
hawkrobe temporarily deployed to cache-upload-forks June 4, 2026 01:54 — with GitHub Actions Inactive
@hawkrobe
hawkrobe force-pushed the coalgebra-graded-connected branch 3 times, most recently from 81adc65 to 5d0e184 Compare June 4, 2026 02:21
@hawkrobe
hawkrobe temporarily deployed to cache-upload-forks June 4, 2026 02:32 — with GitHub Actions Inactive
@hawkrobe
hawkrobe force-pushed the coalgebra-graded-connected branch from 5d0e184 to ac7236c Compare June 4, 2026 03:07
@hawkrobe
hawkrobe temporarily deployed to cache-upload-forks June 4, 2026 03:14 — with GitHub Actions Inactive
@github-actions github-actions Bot removed the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Jun 9, 2026
@mathlib-merge-conflicts mathlib-merge-conflicts Bot added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Jun 18, 2026
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This pull request has conflicts, please merge master and resolve them.

@github-actions github-actions Bot removed the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Jun 24, 2026
@hawkrobe
hawkrobe marked this pull request as draft June 26, 2026 03:53
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mathlib-bors Bot commented Jun 26, 2026

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This pull request is now in draft mode. No active bors state needed cleanup.

While this PR remains draft, bors will ignore commands on this PR. Mark it ready for review before using commands like bors r+ or bors try.

@hawkrobe
hawkrobe marked this pull request as ready for review July 17, 2026 18:12
@hawkrobe

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@YaelDillies I think this is ready for a review, if you have the bandwidth!

@hawkrobe
hawkrobe force-pushed the coalgebra-graded-connected branch from e688ba0 to 58a70be Compare July 18, 2026 00:24
@YaelDillies

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I will try, but I am now on holiday for a month so don't count on me!

@hawkrobe

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enjoy your holiday!!

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