The spectral radius of the Coxeter transformations for a generalized Cartan matrix

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The Inverse of a Real Generalized Cartan Matrix

Abstract. The purpose of this note is to give explicit criteria to determine whether a real generalized Cartan matrix is of finite type, affine type or of hyperbolic type by considering the principal minors and the inverse of the matrix. In particular, it will be shown that a real generalized Cartan matrix is of finite type if and only if it is invertible and the inverse is a positive matrix. A...

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ژورنال

عنوان ژورنال: Mathematische Annalen

سال: 1994

ISSN: 0025-5831,1432-1807

DOI: 10.1007/bf01450490