Tubes in derived categories and cyclotomic factors of the Coxeter polynomial of an algebra.

DOI10.1016/j.jalgebra.2014.08.017zbMath1318.16017OpenAlexW2093802232MaRDI QIDQ743914

Andrzej Mróz, José Antonio de la Peña

Publication date: 1 October 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2014.08.017

zbMATH Keywords

Auslander-Reiten quiverscyclotomic polynomialsstable tubesbounded derived categoriesCoxeter matricesCoxeter polynomialstubular families

Mathematics Subject Classification ID

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Derived categories and associative algebras (16E35)

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A Gram classification of non-negative corank-two loop-free edge-bipartite graphs ⋮ A Gram classification of principal Cox-regular edge-bipartite graphs via inflation algorithm ⋮ Weyl roots and equivalences of integral quadratic forms ⋮ Symbolic computation of strong Gram congruences for Cox-regular positive edge-bipartite graphs with loops ⋮ A Strong Gram Classification of Non-negative Unit Forms of Dynkin Type 𝔸r ⋮ Periodicity in bilinear lattices and the Coxeter formalism ⋮ On mesh geometries of root Coxeter orbits and mesh algorithms for corank two edge-bipartite signed graphs ⋮ A Coxeter spectral classification of positive edge-bipartite graphs. II: Dynkin type \(\mathbb{D}_n\) ⋮ Applications of mesh algorithms and self-dual mesh geometries of root Coxeter orbits to a Horn-Sergeichuk type problem ⋮ Inflation algorithm for loop-free non-negative edge-bipartite graphs of corank at least two ⋮ A computational technique in Coxeter spectral study of symmetrizable integer Cartan matrices ⋮ A Coxeter spectral classification of positive edge-bipartite graphs. I: Dynkin types \(\mathcal{B}_n\), \(\mathcal{C}_n\), \(\mathcal{F}_4\), \(\mathcal{G}_2\), \(\mathbb{E}_6\), \(\mathbb{E}_7\), \(\mathbb{E}_8\) ⋮ Coxeter energy of graphs

Cites Work

• The almost split triangles for perfect complexes over gentle algebras.
• Algebras whose Coxeter polynomials are products of cyclotomic polynomials.
• Tame algebras and integral quadratic forms
• An algorithm for the construction of exceptional modules over tubular canonical algebras.
• Spectral properties of Coxeter transformations and applications
• The spectral radius of the Coxeter transformations for a generalized Cartan matrix
• The trace of the Coxeter matrix and Hochschild cohomology
• Periodic Coxeter matrices
• Generalized standard Auslander-Reiten components
• Parametrizations for integral slope homogeneous modules over tubular canonical algebras.
• An algorithm for the construction of parametrizing bimodules for homogeneous modules over tubular canonical algebras.
• On the periodicity of Coxeter transformations and the non-negativity of their Euler forms
• Generalized canonical algebras and standard stable tubes
• A Coxeter--Gram Classification of Positive Simply Laced Edge-Bipartite Graphs
• Spectral analysis of finite dimensional algebras and singularities
• Eigenvalues of coxeter transformations and the structure of regular componentsof an auslander-reiten quiver
• On the Composition Factors of Periodic Modules
• Concealed-Canonical Algebras and Separating Tubular Families
• Algorithms Determining Matrix Morsifications, Weyl orbits, Coxeter Polynomials and Mesh Geometries of Roots for Dynkin Diagrams
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