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A uniform bound on the nilpotency degree of certain subalgebras of Kac-Moody algebras

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Caprace, Pierre-Emmanuel [UCL]

Let g be a Kac–Moody algebra and b1,b2 be Borel subalgebras of opposite signs. The intersection b=b1∩b2 is a finite-dimensional solvable subalgebra of g. We show that the nilpotency degree of [b,b] is bounded above by a constant depending only on g. This confirms a conjecture of Y. Billig and A. Pianzola [Y. Billig, A. Pianzola, Root strings with two consecutive real roots, Tohoku Math. J. (2) 47 (3) (1995) 391–403].

Document type Article de périodique (Journal article)
Access type Accès restreint
Publication date 2007
Language Anglais
Journal information "Journal of Algebra" - Vol. 317, no. 2, p. 867-876 (2007)
Peer reviewed yes
Publisher Academic Press ((United States) San Diego)
issn 0021-8693
e-issn 1090-266X
Publication status Publié
Affiliation UCL - SST/IRMP - Institut de recherche en mathématique et physique
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Bibliographic reference Caprace, Pierre-Emmanuel. A uniform bound on the nilpotency degree of certain subalgebras of Kac-Moody algebras. In: Journal of Algebra, Vol. 317, no. 2, p. 867-876 (2007)
Permanent URL http://hdl.handle.net/2078.1/94556