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fix table in groups.qmd
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mateuszbaran committed Aug 16, 2024
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---
title: work with groups
toc: true
---

```{julia}
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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

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