Cartan matrices of selfinjective algebras of tubular type
Copyright policy )Cartan matrices of selfinjective algebras of tubular type
The Cartan matrix of a finite dimensional algebra A is an important combinatorial invariant reflecting frequently structural properties of the algebra and its module category. One of the important features of the modular representation theory of finite groups is the nonsingularity of Cartan matrices of the associated group algebras. Recently, the class of all tame self-injective algebras having simply connected Galois coverings and the stable Auslander-Reiten quiver consisting only of stable tubes has been shown to be the class of selfinjective algebras of tubular type. The aim of the paper is to describe the determinants of the Cartan matrices of selfinjective algebras of tubular type and derive some consequences.
group algebras, Matrices over special rings (quaternions, finite fields, etc.), 16g70, Auslander-Reiten quiver, 16g60, Determinants, permanents, traces, other special matrix functions, 16d50, tubular algebra, determinant, Representation type (finite, tame, wild, etc.) of associative algebras, repetitive algebra, Injective modules, self-injective associative rings, Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers, cartan matrix, QA1-939, Cartan matrix, combinatorial invariant, Representations of quivers and partially ordered sets, Galois coverings, secondary 16g20, primary: 15a15, Mathematics, selfinjective algebra
group algebras, Matrices over special rings (quaternions, finite fields, etc.), 16g70, Auslander-Reiten quiver, 16g60, Determinants, permanents, traces, other special matrix functions, 16d50, tubular algebra, determinant, Representation type (finite, tame, wild, etc.) of associative algebras, repetitive algebra, Injective modules, self-injective associative rings, Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers, cartan matrix, QA1-939, Cartan matrix, combinatorial invariant, Representations of quivers and partially ordered sets, Galois coverings, secondary 16g20, primary: 15a15, Mathematics, selfinjective algebra
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