Uniqueness of Chevalley bases for finite-dimensional Lie (super)algebras

From papers

Let p>2p>2 and let a finite-dimensional Lie algebra or Lie superalgebra have an indecomposable Cartan matrix normalized as in the source's normalization convention. A Chevalley basis is an integral basis containing the Chevalley generators, with the normalization determined by that Cartan matrix. Uniqueness of Chevalley bases. There exists only one such analog of the Chevalley basis, up to signs. This extends the stated uniqueness result for ordinary finite-dimensional Lie algebras and the analogous basis considered for Lie superalgebras; the source does not provide evidence here that the assertion has been proved in the stated generality.

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Sources & referencesView supporting material

Primary source

Dimitry Leites and Oleksandr Lozhechnyk, “Inverses of Cartan matrices of Lie algebras and Lie superalgebras”, arXiv:1905.12408 (2019).

Additional references

3 papers in this index state this conjecture (2007–2019). The statement above is taken from the most recent of them; the others are arXiv:0911.0243, arXiv:0710.5149.

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