Submission: 2006, Dec 18
Our goal is to investigate some R-Lie algebras where R is a Laurent polynomial ring in n variables defined over the field of the complex numbers. The main tool is descent theory which permits to classify these objects by non-abelian Galois cohomology. The paper focuses on loop algebras and their Witt-Tits invariants. Since it is related with Serre's conjecture II on Galois cohomology, the n=2 case is especially interesting.
2000 Mathematics Subject Classification: 14L15, 17B67
Keywords and Phrases: Galois cohomology, infinite dimensional Lie algebras, Tits indexes.
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