Exceptional Lie algebra

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In mathematics, an exceptional Lie algebra is a complex simple Lie algebra whose Dynkin diagram is of exceptional (nonclassical) type. [1] There are exactly five of them: ; their respective dimensions are 14, 52, 78, 133, 248. [2] The corresponding diagrams are: [3]

Contents

In contrast, simple Lie algebras that are not exceptional are called classical Lie algebras (there are infinitely many of them).

Construction

There is no simple universally accepted way to construct exceptional Lie algebras; in fact, they were discovered only in the process of the classification program. Here are some constructions:

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References

  1. Fulton & Harris 1991 , Theorem 9.26.
  2. Knapp 2002 , Appendix C, § 2.
  3. Fulton & Harris 1991 , § 21.2.
  4. Tits, Jacques (1966). "Algèbres alternatives, algèbres de Jordan et algèbres de Lie exceptionnelles. I. Construction" (PDF). Indag. Math. 28: 223–237. doi:10.1016/S1385-7258(66)50028-2 . Retrieved 9 August 2023.

Further reading