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Reflection systems and partial root systems
-
Ottmar Loos
and
Erhard Neher
Published/Copyright:
April 2, 2011
Abstract
We develop a general theory of reflection systems and, more specifically, partial root systems which provide a unifying framework for finite root systems, Kac–Moody root systems, extended affine root systems and various generalizations thereof. Nilpotent and prenilpotent subsets are studied in this setting, based on commutator sets and the descending central series. We show that our notion of a prenilpotent pair coincides, for Kac–Moody root systems, with the one defined by Tits in terms of positive systems and the Weyl group.
Keywords.: Reflection systems; partial root systems; affine root systems; extended affine root systems; nilpotent sets of roots
Received: 2009-05-18
Revised: 2009-05-28
Published Online: 2011-04-02
Published in Print: 2011-March
© de Gruyter 2011
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Keywords for this article
Reflection systems;
partial root systems;
affine root systems;
extended affine root systems;
nilpotent sets of roots
Articles in the same Issue
- On the ampleness of the normal bundle of line congruences
- Topological types of 3-dimensional small covers
- Null controllability with constraints on the state for nonlinear heat equations
- Exponential closing property and approximation of Lyapunov exponents of linear cocycles
- Reflection systems and partial root systems
- Todd's maximum-volume ellipsoid problem on symmetric cones
- Refinement of the spectral asymptotics of generalized Krein Feller operators
