[ALGTOP-L] cute proof

Robert Bruner rrb at math.wayne.edu
Tue Dec 1 14:41:13 EST 2009

I just noticed the following proof that the complex numbers C are
algebraically closed, and wonder if anyone has seen it in print anywhere.

  An algebraic extension of C is a unital division algebra over C, say
of dimension n, so induces 
      CP^{n-1} x CP^{n-1} ---> CP^{n-1} 
      y |---> 1 \tensor y + y \tensor 1 
in second integral cohomology.  Since y^n = 0, we must have n=1.

Bob Bruner

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