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Conjugacy problems for "Cartan" subalgebras in infinite dimensional Lie algebras

 Author / Creator
 Yahorau, Uladzimir

Chevalley's theorem on the conjugacy of split Cartan subalgebras is one of the cornerstones of the theory of simple finite dimensional Lie algebras over a field of characteristic 0. Indeed, this theorem affords the most elegant proof that the root system is an invariant of the Lie algebra. The analogous result for symmetrizable KacMoody Lie algebras is the celebrated theorem of Peterson and Kac. However, the methods they used are not suitable for attacking the problem of conjugacy in "higher nullity", i.e. for extended affine Lie algebras (EALA). In the thesis we develop a new cohomological approach which we use to prove 1) conjugacy of Cartan subalgebras in affine KacMoody Lie algebras; 2) conjugacy of maximal abelian addiagonalizable subalgebras (MADs) of EALA of finite type, coming as a part of the structure, where we assume that the centreless core is not isomorphic to sl_2(R), R is a ring of Laurent polynomials in more then 1 variables. We give a counterexample to conjugacy of arbitrary MADs in EALA. Some relevant problems on the lifting of automorphisms are discussed as well.

 Subjects / Keywords

 Graduation date
 Fall 2014

 Type of Item
 Thesis

 Degree
 Doctor of Philosophy

 License
 This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for noncommercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.