[Merged by Bors] - feat: Killing orthogonal complement is complement

[jano-wol]

Killing orthogonal complement is complement

If a Lie algebra has non-singular Killing form then for all ideals, an ideal and its Killing orthogonal complement are complements. This result is needed for the larger proof that a semisimple Lie algebra with irreducible root system is simple.

[github-actions]

PR summary 30e22ac079

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ LieIdeal.isCompl_killingCompl

You can run this locally as follows

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

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for scripts/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/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).

[ocfnash]

I suspect this might be true for any (reflexive, non-degenerate, symmetric) invariant form but I'm happy just to add this key result.

Thanks!

bors d+

[mathlib-bors]

✌️ jano-wol can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[jano-wol]

bors r+

[mathlib-bors]

Pull request successfully merged into master.

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