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Sous-algèbres birégulières d’une algèbre de Kac-Moody-Borcherds

Published online by Cambridge University Press:  22 January 2016

Nicole Bardy
Nicole Bardy*
Affiliation:
Institut Elie Cartan, U.M.R. 9973, Département de mathématiques de l’Université de Nancy I, B.P. 239 54506 Vandoeuvre-lès-Nancy Cedex, France, Nicole.Bardy-Panse@iecn.u-nancy.fr
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Abstract

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Let be a Kac-Moody-Borcherds algebra on a field associated to a symetrizable matrix and with Cartan subalgebra . Let be an ad -invariant subalgebra such that the restriction to of the standard bilinear form is nondegenerate. We show that the root system Ψ of is a subsystem according to [Ba] of . Moreover, if a subsystem Ω satisfies some conditions (i.e. Ω is “réduit et presque-clos”) of Ψ, we construct inside of a Kac-Moody-Borcherds algebra with root system Ω.

Let k be a subfield of . We prove similar results in the case of an action of a finite group of k-semi-automorphisms. In particular, we obtain a generalization to the Kac-Moody case of a result by Borel and Tits.

Let be an almost-k-split form of a Kac-Moody algebra. We construct a Kac-Moody k-algebra with root system similar to the system of (save on some multiples of certain roots).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 156 , 1999 , pp. 1 - 83
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1999

References

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