On the classification of semisimple Lie algebras
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Date
2010Author
Kurujyibwami, Celestin
Type
ThesisLanguage
enMetadata
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Lie algebra over a field F (F= [; lis a vector space Lover F equipped with a skew symmetric
bilinear operation called the Lie bracket, which satisfied the Jacobi identity.
Lie algebras, have Jordan decomposition into semisimple and nilpotent parts, with representation
theory of nilpotent Lie algebras being intractable in general. The finite dimensional
representation and classification of semisimple Lie algebras are completely understood, after
work ofElie Cartan.
A classification of semisimple Lie algebras L is analyzed by choosing a Cartan subalgebra which
is essentially a generic maximal subalgebra H of L on which the Lie bracket is zero (abelian).
The representation of L is decomposed into weight spaces which are eigen spaces for the action
of H (root space decomposition). From which the analysis of representation is easily understood
by the possible weights which can occur (root system).
The classification of semisimple Lie algebras by Dynkin gives the four classical Lie algebras and
five exceptional simple Lie algebras over the finite algebraically field of characteristic zero.
Citation
M.Sc (Pure Mathematics)Sponsorhip
University of NairobiPublisher
School of Mathematics, University of Nairobi
Description
Master of Science Thesis