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EDIT: After looking into the history more closely, I think it's fairly certain that the correct answer to the question is Calvin Moore. (See my added text below.) The question is interesting and l …

[EDIT] These groups have been studied for a long time from various viewpoints, so there is a long paper-trail. I'd emphasize however that working over the complex numbers is usually similar to workin …

Here's a small follow-up on Matsumoto's thesis, which deals essentially with the congruence subgroup problem for Chevalley (split) algebraic groups. This followed work by Bass-Milnor-Serre, but in t …

Just after the limited work by Bass-Milnor-Serre was published, the work of Moore made possible a major improvement by H. Matsumoto in his Paris thesis here, treating uniformly all the split (Chevalle …

Typically the homomorphism here $K_0 \rightarrow G_0$ fails to be surjective. This shows up in a wide range of examples involving group algebras of finite groups (over fields of characteristic dividi …

EDIT: My beliefs about all of this are subject to change, since it's been decades since I was involved in this literature. I apologize for adding to the clutter here, but the question itself (though …

An offbeat question involving Milnor's $K_2$ has come up recently. Start with an algebraically closed field $F$ (perhaps required to be of characteristic 0). Let $G$ be a connected, simply connected …