From 8a4797cd81b99fdf31905586e180ea10219d0cca Mon Sep 17 00:00:00 2001 From: Mateusz Baran Date: Fri, 16 Aug 2024 11:36:04 +0200 Subject: [PATCH] fix table in groups.qmd --- tutorials/groups.qmd | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/tutorials/groups.qmd b/tutorials/groups.qmd index fd5749c7b..c089b64a4 100644 --- a/tutorials/groups.qmd +++ b/tutorials/groups.qmd @@ -1,5 +1,6 @@ --- title: work with groups +toc: true --- ```{julia} @@ -220,19 +221,18 @@ Now, `q1_m` and `q2_m` are different due to non-invariance of the metric connect The following table outlines invariance of `exp` and `log` of various groups. +````{=commonmark} | Group | Zero torsion connection | Invariant | -| --- | --- | --- | +|---|---|---| | `ProductGroup` | Product of connections in each submanifold | Yes if both connections are invariant separately, otherwise no | | `SemidirectProductGroup` | Same as underlying product | ❌ | | `TranslationGroup` | `CartanSchoutenZero` | ✅ | -| `CircleGroup` | `CartanSchoutenZero` |✅| +| `CircleGroup` | `CartanSchoutenZero` | ✅ | | `GeneralLinearGroup` | Metric connection from the left invariant metric induced from the standard basis on the Lie algebra | ❌ | | `GeneralUnitaryMultiplicationGroup` | `CartanSchoutenZero` (explicitly) | ✅ | | `HeisenbergGroup` | `CartanSchoutenZero` | ✅ | | `SpecialLinearGroup` | Same as `GeneralLinear` | ❌ | - -: Invariance of `exp` and `log` for various groups {#tbl-exp-log-inv} - +```` ## Literature