MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top
This is a lemma in Ancohea's paper…. I can not understand the proof. – yanyu Jun 3 '13 at 4:43
Hmm, the proof of the lemma in that paper seems to suggest Ancohea assumes the division algebra is finite-dimensional over the center, but this is never clearly stated earlier in the paper. How about the following 1-sentence proof: the commutators over $k$ span the space of commutators over $\overline{k}$, so it suffices to treat the case of a matrix algebra, which you can treat by bare hands. QED – user30180 Jun 3 '13 at 6:22

Yes because the division ring generated by commutators is invariant under all inner automorphisms and the result follows from Cartan-Brauer-Hua.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.