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Results tagged with algebraic-k-theory
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user 4231
7
votes
Bass's paper "Symplectic groups and modules", used in proof of the congruence subgroup prope...
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 …
- 52.9k
2
votes
0
answers
254
views
Certain central extensions of simply connected simple algebraic groups
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 …
- 52.9k
9
votes
Accepted
Normal subgroups of $SL_2$ of a polynomial ring
[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 …
- 52.9k
11
votes
Who first noticed that the Hilbert symbol is a Steinberg symbol ?
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 …
- 52.9k
6
votes
Accepted
f.g. modules vs. f.g. projective modules
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 …
- 52.9k
4
votes
Universal cover of SL2(R) admits no central extensions?
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 …
- 52.9k
8
votes
Symplectic Steinberg group
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 …
- 52.9k