Invariant symmetric bilinear forms for reflection groups

Kürner B, Neeb KH (2001)

Publication Type: Journal article, Original article

Publication year: 2001

Journal

Journal of Geometry Birkhauser Verlag

Publisher: Birkhauser Verlag

Book Volume: 71

Pages Range: 99-127

Journal Issue: 1

DOI: 10.1007/s00022-001-8556-2

Abstract

In this paper we describe a connection between Vinberg's criterion for the existence of an invariant symmetric bilinear form for a geometric representation of a Coxeter groups and other criteria which are formulated in terms of conjugation invariant sets of reflections generating a given group. Similar methods lead to the result that every non-symmetrizable Kac--Moody Lie algebra contains a non-symmetrizable subalgebra of rank 3. Finally we explain how the results for symmetric bilinear forms can also be obtained for skew-symmetric forms.

Authors with CRIS profile

Karl Hermann Neeb Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)

Involved external institutions

Technische Universität Darmstadt DE Germany (DE)

How to cite

APA:

Kürner, B., & Neeb, K.H. (2001). Invariant symmetric bilinear forms for reflection groups. Journal of Geometry, 71(1), 99-127. https://dx.doi.org/10.1007/s00022-001-8556-2

MLA:

Kürner, Bettina, and Karl Hermann Neeb. "Invariant symmetric bilinear forms for reflection groups." Journal of Geometry 71.1 (2001): 99-127.

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