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On the Coxeter polynomials of wild stars

โœ Scribed by Piroska Lakatos

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
119 KB
Volume
293
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

The spectral radius of a Coxeter transformation which plays an important role in the representation theory of hereditary algebras [see V. Dlab, C.M. Ringel, Eigenvalues of Coxeter transformations and the GelfandยฑKirillov dimension of the preprojective algebras, Proc. AMS 83 (1990) 228ยฑ232] is its important invariant. This paper provides both upper and lower bounds for the spectral radii of the Coxeter transformations of wild stars (i.e. trees that have a single branching point and are neither of Dynkin nor of Euclidean type). In addition, the paper determines limit of the spectral radii of particular inยฎnite sequences of wild stars and shows dierent classes of graphs with the same limit. The basic idea is to reduce the study of spectral radii of trees to the spectral radii of particular valued graphs with indeยฎnite type of associated generalized Cartan matrix.

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