Quadratic algorithm to compute the Dynkin type of a positive definite quasi-Cartan matrix

DOI10.1090/mcom/3559zbMath1468.15019OpenAlexW3026216118MaRDI QIDQ5131008

Bartosz Makuracki, Andrzej Mróz

Publication date: 31 October 2020

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/mcom/3559

zbMATH Keywords

Cartan matrixGram matrixDynkin diagramintegral quadratic forminflation algorithmquasi-Cartan matrix

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Symbolic computation and algebraic computation (68W30) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Positive matrices and their generalizations; cones of matrices (15B48) Quadratic and bilinear forms, inner products (15A63) Canonical forms, reductions, classification (15A21) Signed and weighted graphs (05C22)

Related Items (5)

Weyl roots and equivalences of integral quadratic forms ⋮ Isotropy groups of the action of orthogonal similarity on symmetric matrices ⋮ A Coxeter spectral classification of positive edge-bipartite graphs. II: Dynkin type \(\mathbb{D}_n\) ⋮ Polynomial-time Classification of Skew-symmetrizable Matrices with a Positive Definite Quasi-Cartan Companion ⋮ Congruence of rational matrices defined by an integer matrix

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