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Lie algebras and the transition to affine lie algebras in two dimensional maximal supergravity

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 semi-simple 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 Kac-Moody 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 semi-simple Lie algebra. The affine Lie algebra can be roughly be seen as an infinite tower of a semi-simple Lie algebra. This means that an affine Lie algebra can be constructed as the affine extension of a semi-simple Lie algebra. Lie algebras appear in a slightly different manner in physics. They are closely related to symmetries. A close look at space-time symmetries and supersymmetry will result in a Super-Poincar'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 Kaluza-Klein 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: http://fse.studenttheses.ub.rug.nl/id/eprint/11142

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