Exceptional Lie algebra g2 and its representations

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2022-9-01

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Kayakökü, Mehmet Mustafa

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In the classification of complex simple Lie algebras, there are five of them whose Dynkin diagrams are of exceptional type. The Lie algebra g_2 has the smallest dimension among these exceptional Lie algebras and together with its corresponding Lie group G_2, it plays an important role in differential geometry, mathematical physics, and modern string theory. In this thesis after a general introduction to Lie algebras, we show the classification of complex simple ones. Afterward, we give several constructions of the exceptional Lie algebra g_2 and investigate its fundamental representations.

Subject Keywords

Lie algebra, Lie group, exceptional Lie algebra, exceptional Lie group

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https://hdl.handle.net/11511/99442

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

M. M. Kayakökü, “Exceptional Lie algebra g2 and its representations,” M.S. - Master of Science, Middle East Technical University, 2022.