On infinite root systems

Moody, R. V.; Pianzola, A.

doi:10.1090/S0002-9947-1989-0964901-8

On infinite root systems
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by R. V. Moody and A. Pianzola PDF

Trans. Amer. Math. Soc. 315 (1989), 661-696 Request permission

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.

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