On infinite root systems-Reference-Cited by-同舟云学术

On infinite root systems

Published:1989 Issue:2 Volume:315 Page:661-696
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Moody R. V.,Pianzola A.

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1989-315-02/S0002-9947-1989-0964901-8/S0002-9947-1989-0964901-8.pdf

Reference14 articles.

1. Actualit\'{e}s Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337;Bourbaki, N.,1968

2. C. Caratheodory, Theory of functions, vol. 2, Chelsea, New York, 1960.

3. Pure and Applied Mathematics, Vol. 28;Carter, Roger W.,1972

4. Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences];Conway, J. H.,1988

5. A note on subgroups generated by reflections in Coxeter groups;Deodhar, Vinay V.;Arch. Math. (Basel),1989

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