Spectral properties of Coxeter transformations and applications

DOI10.1007/BF01189130zbMath0687.16017OpenAlexW2055120715MaRDI QIDQ1262929

K. Appert

Publication date: 1990

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01189130

zbMATH Keywords

Cartan matrixeigenvaluewild algebrastranslationpath algebraAuslander-Reiten quiverindecomposable moduleregular componentsCoxeter matrixwild casepreinjective componentpreprojective componentfinite connected oriented graphfinite dimensional hereditary k-algebra

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Eigenvalues, singular values, and eigenvectors (15A18) Quadratic and bilinear forms, inner products (15A63) Canonical forms, reductions, classification (15A21) Representation theory of associative rings and algebras (16Gxx)

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On spectral radii of Coxeter transformations., On the number of terms in the middle of almost split sequences over tame algebras, A Gram classification of non-negative corank-two loop-free edge-bipartite graphs, On the Coxeter transformation of a wild algebra, The spectral radius of the Coxeter transformations for a generalized Cartan matrix, Elementary stones, Characterizations of strongly simply connected polynomial growth algebras, Coxeter transformations of the derived categories of coherent sheaves, Characterizations of tame algebras with separating families of almost cyclic coherent components, Periodicity in bilinear lattices and the Coxeter formalism, On the Mahler measure of the Coxeter polynomial of an algebra., Bounds related to Coxeter spectral measures of graphs, Noetherianity and Gelfand-Kirillov dimension of components., Cluster-cyclic quivers with three vertices and the Markov equation. (With an appendix by Otto Kerner)., Conjugacy relation on Coxeter elements, A Chebysheff recursion formula for Coxeter polynomials, Tubes in derived categories and cyclotomic factors of the Coxeter polynomial of an algebra., The Coxeter polynomial for a one point extension algebra., The spectral classes of unicyclic graphs, Mono orbits, epi orbits and elementary vertices of representation infinite quivers, Minimal approximations, orbital elementary modules, and orbit algebras of regular modules, Stable representations of quivers.

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• Linear Transformations with Invariant Cones