Journal of Lie Theory

no. 3
Normalisers of Abelian Ideals of a Borel Subalgebra and Z-Gradings of a Simple Lie Algebra
Journal of Lie Theory, Volume 26 (2016) no. 3, pp. 659-672
Let g be a simple Lie algebra and Ab the poset of all abelian ideals of a fixed Borel subalgebra of g. If a is an element of Ab, then the normaliser of a is a standard parabolic subalgebra of g. We give an explicit description of the normaliser for a class of abelian ideals that includes all maximal abelian ideals. We also elaborate on a relationship between abelian ideals and Z-gradings of g associated with their normalisers.
DOI: 10.5802/jolt.904
Classification: 17B20, 17B22, 20F55
Keywords: Root system, Borel subalgebra, minuscule element, abelian ideal 
@article{JOLT_2016_26_3_a2,
     author = {D. I. Panyushev},
     title = {Normalisers of {Abelian} {Ideals} of a {Borel} {Subalgebra} and {Z-Gradings} of a {Simple} {Lie} {Algebra}},
     journal = {Journal of Lie Theory},
     pages = {659--672},
     year = {2016},
     volume = {26},
     number = {3},
     doi = {10.5802/jolt.904},
     zbl = {1406.17018},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.904/}
}
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D. I. Panyushev. Normalisers of Abelian Ideals of a Borel Subalgebra and Z-Gradings of a Simple Lie Algebra. Journal of Lie Theory, Volume 26 (2016) no. 3, pp. 659-672. doi: 10.5802/jolt.904

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