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Chapter VI of my old Springer Lecture Notes in Mathematics 789 Arithmetic Groups (1980) is in English and gives a version of H. Matsumoto's and C. Moore's arguments for the subgroups of $\operatorname …

The question is not well-formulated (for instance, it's not clear what you mean by "the right chevalley basis", and Chevalley is a proper name). Most important, your third sentence doesn't make sens …

First of all, I'd inquire what role the characteristic of the field plays here. It's true that the finite twisted groups rely on characteristics 2, 3 especiallu, but infinite twisted groups include …

The question shows some confusion but also illustrates the difficulty of working with the Spin groups (the universal groups of types $B_\ell$ and $D_\ell$). It's easier to work with the single Lie al …

There are probably multiple ways to see that $G(\mathbb{R})$ is non-compact when $G$ is a Chevalley group (in either the narrow sense of Chevalley or the broader sense of Steinberg's lectures). One …

In the original sense, Chevalley groups are generated by copies of the additive group of the field and are in fact simple as abstract groups if the field is not too small. (This was the motive for …