[Merged by Bors] - feat(linear_algebra/clifford_algebra): the clifford algebra is isomorphic as a module to the exterior algebra #11468
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While this work is incomplete, it is sufficient to illustrate the example in the ICACGA paper. The full version will eventually integrate into mathlib as part of leanprover-community/mathlib#11468.
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…phic as a module to the exterior algebra (#11468) The key result here is ```lean /-- The module isomorphism to the exterior algebra -/ def equiv_exterior [invertible (2 : R)] : clifford_algebra Q ≃ₗ[R] exterior_algebra R M := ``` There are a handful of intermediate definitions that are needed to get here that are missing lots of useful (but difficult) API lemmas, but I don't expect to have time to address those for a while. Probably the main missing result is that `equiv_exterior` preserves reversion.
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…phic as a module to the exterior algebra (#11468) The key result here is ```lean /-- The module isomorphism to the exterior algebra -/ def equiv_exterior [invertible (2 : R)] : clifford_algebra Q ≃ₗ[R] exterior_algebra R M := ``` There are a handful of intermediate definitions that are needed to get here that are missing lots of useful (but difficult) API lemmas, but I don't expect to have time to address those for a while. Probably the main missing result is that `equiv_exterior` preserves reversion.
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…phic as a module to the exterior algebra (#11468) The key result here is ```lean /-- The module isomorphism to the exterior algebra -/ def equiv_exterior [invertible (2 : R)] : clifford_algebra Q ≃ₗ[R] exterior_algebra R M := ``` There are a handful of intermediate definitions that are needed to get here that are missing lots of useful (but difficult) API lemmas, but I don't expect to have time to address those for a while. Probably the main missing result is that `equiv_exterior` preserves reversion.
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…phic as a module to the exterior algebra (#11468) The key result here is ```lean /-- The module isomorphism to the exterior algebra -/ def equiv_exterior [invertible (2 : R)] : clifford_algebra Q ≃ₗ[R] exterior_algebra R M := ``` There are a handful of intermediate definitions that are needed to get here that are missing lots of useful (but difficult) API lemmas, but I don't expect to have time to address those for a while. Probably the main missing result is that `equiv_exterior` preserves reversion.
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…phic as a module to the exterior algebra (#11468) The key result here is ```lean /-- The module isomorphism to the exterior algebra -/ def equiv_exterior [invertible (2 : R)] : clifford_algebra Q ≃ₗ[R] exterior_algebra R M := ``` There are a handful of intermediate definitions that are needed to get here that are missing lots of useful (but difficult) API lemmas, but I don't expect to have time to address those for a while. Probably the main missing result is that `equiv_exterior` preserves reversion.
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…phic as a module to the exterior algebra (#11468) The key result here is ```lean /-- The module isomorphism to the exterior algebra -/ def equiv_exterior [invertible (2 : R)] : clifford_algebra Q ≃ₗ[R] exterior_algebra R M := ``` There are a handful of intermediate definitions that are needed to get here that are missing lots of useful (but difficult) API lemmas, but I don't expect to have time to address those for a while. Probably the main missing result is that `equiv_exterior` preserves reversion.
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The key result here is
There are a handful of intermediate definitions that are needed to get here that are missing lots of useful (but difficult) API lemmas, but I don't expect to have time to address those for a while.
Probably the main missing result is that
equiv_exteriorpreserves reversion.bibtoolonreferences.bib#16606bilin_form.to_quadratic_form#16616