It is said that there is a proof of fundamental theorem of algebra using Lie Theory. I have seen this claim at various places. But I could never find such a proof. Can anybody help me out?
Fundamental theorem of algebra using Lie Theory
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complex-analysis
lie-groups
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0@Qiaochu: I wanted the tag complex-variables as Fun. Thm. is a theorem about complex numbers. But I am a new user and I cannot create tags; so I went for complex-analysis. – 2010-08-12
2 Answers
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The references can be found in the comments here:
For those who don't know it, the (well, a) Lie-theoretic proof of Fund. Thm. of Algbera due to Witt is on p. 245 of the book "Numbers" by Ebbinghaus et al. – KConrad Aug 6 at 4:44
Witt's Lie-theoretic proof of Fund. Thm. of Algbera seems to be Witt (Ernst), Über einen Satz von Ostrowski, Arch. Math. (Basel) 3, (1952). 334. – Chandan Singh Dalawat Aug 6 at 6:11
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1KCd: +x! To unpack a couple of statements: "if R^n were a degree n extension field R[x]/(p(x)=0 then (...) "; unit group is connected and, for n>2, simply connected because it is (R^n minus one point). – 2019-04-16
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Muad: Are you talking about this www.fc.up.pt/mp/jcsantos/PDF/artigos/FTA.pdf
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0@Chandru1, @George: Removed discussion of an interesting, but clearly off-topic paper. – 2010-08-14