Abstract
The exceptional groups, or more precisely, the exceptional Lie algebras, were made explicit in Elie Cartan’s thesisl of 1894 by his classification of the complex semisimple Lie algebras. Cartan noted that in addition to the four classical Lie algebras A n, B n, C n and D n, respectively associated with the classical Lie groups SU n+1, SO 2n+1, Sp 2n and SO 2n, there were five exceptional Lie algebras, G 2, F 4, E 6, E 7 and E 8 whose adjoint irreducible representations were of degree 14, 52, 78, 133 and 248 respectively.
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Wybourne, B.G. (1991). Group Structures and the Interacting Boson Approximation for Nuclei. In: Gruber, B., Biedenharn, L.C., Doebner, H.D. (eds) Symmetries in Science V. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3696-3_28
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DOI: https://doi.org/10.1007/978-1-4615-3696-3_28
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