Cartan matrices and Grothendieck groups of stable categories (Q1180652)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Cartan matrices and Grothendieck groups of stable categories |
scientific article; zbMATH DE number 26266
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cartan matrices and Grothendieck groups of stable categories |
scientific article; zbMATH DE number 26266 |
Statements
Cartan matrices and Grothendieck groups of stable categories (English)
0 references
27 June 1992
0 references
The main result asserts that if \(A\) is a finite dimensional algebra over a field \(K\) and \(\widehat A\) its repetitive algebra, then \(K_ 0(\text{mod} \widehat A)\simeq K_ 0(\text{mod} A)\) if and only if \(\text{det }C=\pm 1\), \(C\) being the Cartan matrix of \(A\).
0 references
finite dimensional algebra
0 references
repetitive algebra
0 references
Cartan matrix
0 references
