Cartan subspaces of symmetric Lie algebras
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- by J. Lepowsky and G. W. McCollum
- Trans. Amer. Math. Soc. 216 (1976), 217-228
- DOI: https://doi.org/10.1090/S0002-9947-1976-0404361-X
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Abstract:
A symmetric Lie algebra is defined, following J. Dixmier, to be a Lie algebra $\mathfrak {g}$ with a decomposition $\mathfrak {g} = \mathfrak {k} \oplus \mathfrak {p}$ such that $\mathfrak {k}$ is a subalgebra of $\mathfrak {g},[\mathfrak {k},\mathfrak {p}] \subset \mathfrak {p}$ and $[\mathfrak {p},\mathfrak {p}] \subset \mathfrak {k}$. A definition of Cartan subspace of a symmetric Lie algebra is given, and a theory is presented which parallels the standard theory of Cartan subalgebras of Lie algebras, and which generalizes the classical results for real and complex semisimple symmetric Lie algebras.References
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Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 216 (1976), 217-228
- MSC: Primary 17B05
- DOI: https://doi.org/10.1090/S0002-9947-1976-0404361-X
- MathSciNet review: 0404361