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## Derived endo-discrete artin algebras

### Tom 105 / 2006

Colloquium Mathematicum 105 (2006), 297-310 MSC: 16G60, 18E30. DOI: 10.4064/cm105-2-10

#### Streszczenie

Let ${\mit\Lambda}$ be an artin algebra. We prove that for each sequence $(h_{i})_{i\in \mathbb{Z}}$ of non-negative integers there are only a finite number of isomorphism classes of indecomposables $X\in \mathcal{D}^{\rm b}({\mit\Lambda} ),$ the bounded derived category of ${\mit\Lambda}$, with $\mathop{\rm length}\nolimits _{E(X)}H^{i}(X)=h_{i}$ for all $i\in \mathbb{Z}$ and $E(X)$ the endomorphism ring of $X$ in $\mathcal{D}^{\rm b}({\mit\Lambda} )$ if and only if $\mathcal{D}^{\rm b}(\mathop{\rm Mod}\nolimits {\mit\Lambda} )$, the bounded derived category of the category $\mathop{\rm Mod}\nolimits {\mit\Lambda}$ of all left ${\mit\Lambda}$-modules, has no generic objects in the sense of [4].

#### Autorzy

• Raymundo BautistaInstituto de Matemáticas