On root Fernando-Kac subalgebras of finite type

  • Let g be a finite-dimensional Lie algebra and M be a g-module. The Fernando-Kac subalgebra of g associated to M is the subset gsubsetg of all elements xin g which act locally finitely on M. A subalgebra lsubset g for which there exists an irreducible module M with g[M]=l is called a Fernando-Kac subalgebra of g. A Fernando-Kac subalgebra of g is of finite type if in addition M can be chosen to have finite Jordan-Hölder l-multiplicities. Under the assumption that g is simple, I. Penkov has conjectured an explicit combinatorial criterion describing all Fernando-Kac subalgebras of finite type which contain a Cartan subalgebra. The thesis proves this conjecture for g not equal to E_8.

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Publishing Institution:IRC-Library, Information Resource Center der Jacobs University Bremen
Granting Institution:Jacobs Univ.
Author:Todor Milev
Referee:Ivan Petkov, Peter Fiebig, Vera Serganova
Advisor:Ivan Petkov
Persistent Identifier (URN):urn:nbn:de:101:1-2013052411047
Document Type:PhD Thesis
Date of Successful Oral Defense:2010/10/28
Date of First Publication:2010/11/29
PhD Degree:Mathematics
School:SES School of Engineering and Science
Library of Congress Classification:Q Science / QA Mathematics (incl. computer science) / QA150-272.5 Algebra
Call No:Thesis 2010/28

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