Real forms of embeddings of maximal reductive subalgebras of the complex simple Lie algebras of rank up to 8

@article{deGraaf2019RealFO,
  title={Real forms of embeddings of maximal reductive subalgebras of the complex simple Lie algebras of rank up to 8},
  author={Willem A. de Graaf and Alessio Marrani},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2019},
  volume={53}
}
We consider the problem of determining the noncompact real forms of maximal reductive subalgebras of complex simple Lie algebras. We briefly describe two algorithms for this purpose that are taken from the literature. We discuss applications in theoretical physics of these embeddings. The supplementary material to this paper contains the tables of embeddings that we have obtained for all real forms of the semisimple Lie algebras of rank up to 8. 

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References

SHOWING 1-10 OF 74 REFERENCES

Constructing semisimple subalgebras of real semisimple Lie algebras

Computing the real Weyl group

Finite-Dimensional Lie Algebras and Their Representations for Unified Model Building

We give information about finite-dimensional Lie algebras and their representations for model building in 4 and 5 dimensions; e.g., conjugacy classes, types of representations, Weyl dimensional

CLASSIFICATION OF SEMISIMPLE SUBALGEBRAS OF SIMPLE LIE ALGEBRAS.

An explicit classification of the semisimple complex Lie subalgebras of the simple complex Lie algebras is given for algebras up to rank 6. The notion of defining vector, introduced by Dynkin and

Conformal and Quasiconformal Realizations¶of Exceptional Lie Groups

Abstract: We present a nonlinear realization of E8(8) on a space of 57 dimensions, which is quasiconformal in the sense that it leaves invariant a suitably defined “light cone” in ℝ57. This

The semisimple subalgebras of exceptional Lie algebras

. Dynkin classified the maximal semisimple subalgebras of exceptional Lie algebras up to conjugacy, but only classified the simple subalgebras up to the coarser relation of linear conjugacy. In the

volume 652 of Contemp

  • Math., pages 75–89. Amer. Math. Soc., Providence, RI,
  • 2015
...