On Infinite Root Systems

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1989Publisher:JSTORJournal:Transactions of the American Mathematical Society, volume 315, page 661 (issn: 0002-9947,

Copyright policy )Funded by:NSERC | unidentified

Authors: Moody, R. V.; Pianzola, A.;

doi: 10.2307/2001300 , 10.1090/s0002-9947-1989-0964901-8

On Infinite Root Systems

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Abstract

We define in an axiomatic fashion the concept of a set of root data that generalizes the usual concept of root system of a Kac-Moody Lie algebra. We study these objects from a purely formal and geometrical point of view as well as in relation to their associated Lie algebras. This leads to a coherent theory of root systems, bases, subroot systems, Lie algebras defined by root data, and subalgebras.

Keywords

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, set of root data, Kac-Moody Lie algebra, Supersymmetric field theories in quantum mechanics, root system, Weyl groups

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