Boer, M. H. (2013) Lie algebras and the transition to affine lie algebras in two dimensional maximal supergravity. Bachelor's Thesis, Physics.

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Abstract
Finite dimensional simple and semisimple Lie algebras will be categorized with the help of Hasse diagrams and Cartan matrices. These results will be used in the construction of a very specific KacMoody algebra: the affine Lie algebra. This infinite dimensional highly structured Lie algebra can be constructed using the generalized Cartan matrix. An affine Lie algebra is closely related to a semisimple Lie algebra. The affine Lie algebra can be roughly be seen as an infinite tower of a semisimple Lie algebra. This means that an affine Lie algebra can be constructed as the affine extension of a semisimple Lie algebra. Lie algebras appear in a slightly different manner in physics. They are closely related to symmetries. A close look at spacetime symmetries and supersymmetry will result in a SuperPoincar'e algebra. Supersymmetry can then be gauged to construct a supergravitational theory. Maximal supergravity is a supergravity theory with as many supersymmetry generators as physically possible. It can most easily be obtained by KaluzaKlein dimensional reduction of eleven dimensional supergravity.
Item Type:  Thesis (Bachelor's Thesis) 

Degree programme:  Physics 
Thesis type:  Bachelor's Thesis 
Language:  English 
Date Deposited:  15 Feb 2018 07:53 
Last Modified:  15 Feb 2018 07:53 
URI:  https://fse.studenttheses.ub.rug.nl/id/eprint/11142 
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