Maurer Cartan equations I believe there is a mistake in the Maurer Cartan equations as they are mentioned in the section The minus signs should be plus signs Starting from begin align text d pi theta i varepsilon i text d varepsilon i omega k i varepsilon k end align and computing as indicated on the aforementioned article if is found that as well as Using the linear independence of the functions yields the Maurer Cartan equations but with plus signs between the terms instead of the minus signs on the article