Cartan matrices of selfinjective algebras of tubular type

• Autorzy: Jerzy Białkowski
• Języki publikacji: EN

Abstrakty

EN

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. For example, one of the important features of the modular representation theory of finite groups is the nonsingularity of Cartan matrices of the associated group algebras (Brauer’s theorem). Recently, the class of all tame selfinjective 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, that is, the orbit algebras $$ \hat B$$ /G of the repetitive algebras $$ \hat B$$ of tubular algebras B with respect to the actions of admissible groups G of automorphisms of $$ \hat B$$ . The aim of the paper is to describe the determinants of the Cartan matrices of selfinjective algebras of tubular type and derive some consequences.

Słowa kluczowe

EN

Cartan matrix; determinant; selfinjective algebra; repetitive algebra; tubular algebra; Primary: 15A15; 16D50; 16G60; Secondary 16G20; 16G70

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 1
• Strony: 123-142

Daty

wydano

2004-03-01

online

2004-03-01

Twórcy

autor

Jerzy Białkowski

• Nicolaus Copernicus University

Bibliografia

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Identyfikatory

DOI

10.2478/BF02475956