Periodicity in bilinear lattices and the Coxeter formalism

DOI10.1016/j.laa.2015.11.021zbMath1329.15054OpenAlexW2197491934MaRDI QIDQ905716

Andrzej Mróz, José Antonio de la Peña

Publication date: 28 January 2016

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2015.11.021

zbMATH Keywords

quadratic formcirculant matrixCoxeter polynomialcyclotomic polynomialbilinear latticestable tubetubular family

Mathematics Subject Classification ID

Grothendieck groups, (K)-theory, etc. (16E20) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Polynomials in number theory (11C08) Representations of quivers and partially ordered sets (16G20) Quadratic and bilinear forms, inner products (15A63) Matrices of integers (15B36) Derived categories and associative algebras (16E35)

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Uses Software

• TUBULAR

Cites Work

• On the Mahler measure of the Coxeter polynomial of an algebra.
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• The almost split triangles for perfect complexes over gentle algebras.
• Algebras whose Coxeter polynomials are products of cyclotomic polynomials.
• Tubes in derived categories and cyclotomic factors of the Coxeter polynomial of an algebra.
• Tame algebras and integral quadratic forms
• Spectral properties of Coxeter transformations and applications
• The spectral radius of the Coxeter transformations for a generalized Cartan matrix
• Wild canonical algebras
• The trace of the Coxeter matrix and Hochschild cohomology
• Periodic Coxeter matrices
• Generalized standard Auslander-Reiten components
• The Dynkin type of a non-negative unit form.
• Numeric and mesh algorithms for the Coxeter spectral study of positive edge-bipartite graphs and their isotropy groups
• On the periodicity of Coxeter transformations and the non-negativity of their Euler forms
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• Mesh Algorithms for Coxeter Spectral Classification of Cox-regular Edge-bipartite Graphs with Loops, I. Mesh Root Systems
• Mesh Algorithms for Coxeter Spectral Classification of Cox-regular Edge-bipartite Graphs with Loops, II. Application to Coxeter Spectral Analysis
• Algorithms for Isotropy Groups of Cox-regular Edge-bipartite Graphs
• A Coxeter--Gram Classification of Positive Simply Laced Edge-Bipartite Graphs
• Mesh Algorithms for Solving Principal Diophantine Equations, Sand-glass Tubes and Tori of Roots
• Spectral analysis of finite dimensional algebras and singularities
• Eigenvalues of coxeter transformations and the structure of regular componentsof an auslander-reiten quiver
• Concealed-Canonical Algebras and Separating Tubular Families
• Congruences of Edge-bipartite Graphs with Applications to Grothendieck Group Recognition I. Inflation Algorithm Revisited*
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