Derived endo-discrete artin algebras

Raymundo Bautista. "Derived endo-discrete artin algebras." Colloquium Mathematicae 105.2 (2006): 297-310. <http://eudml.org/doc/283566>.

@article{RaymundoBautista2006,
abstract = {Let Λ be an artin algebra. We prove that for each sequence $(h_\{i\})_\{i∈ ℤ\}$ of non-negative integers there are only a finite number of isomorphism classes of indecomposables $X ∈ ^\{b\}(Λ)$, the bounded derived category of Λ, with $length_\{E(X)\}H^\{i\}(X) = h_\{i\}$ for all i ∈ ℤ and E(X) the endomorphism ring of X in $^\{b\}(Λ)$ if and only if $^\{b\}(Mod Λ)$, the bounded derived category of the category $Mod Λ$ of all left Λ-modules, has no generic objects in the sense of [4].},
author = {Raymundo Bautista},
journal = {Colloquium Mathematicae},
keywords = {Artin algebras; lift categories; derived categories; generic complexes; endo-discrete algebras; endofinite modules},
language = {eng},
number = {2},
pages = {297-310},
title = {Derived endo-discrete artin algebras},
url = {http://eudml.org/doc/283566},
volume = {105},
year = {2006},
}

TY - JOUR
AU - Raymundo Bautista
TI - Derived endo-discrete artin algebras
JO - Colloquium Mathematicae
PY - 2006
VL - 105
IS - 2
SP - 297
EP - 310
AB - Let Λ be an artin algebra. We prove that for each sequence $(h_{i})_{i∈ ℤ}$ of non-negative integers there are only a finite number of isomorphism classes of indecomposables $X ∈ ^{b}(Λ)$, the bounded derived category of Λ, with $length_{E(X)}H^{i}(X) = h_{i}$ for all i ∈ ℤ and E(X) the endomorphism ring of X in $^{b}(Λ)$ if and only if $^{b}(Mod Λ)$, the bounded derived category of the category $Mod Λ$ of all left Λ-modules, has no generic objects in the sense of [4].
LA - eng
KW - Artin algebras; lift categories; derived categories; generic complexes; endo-discrete algebras; endofinite modules
UR - http://eudml.org/doc/283566
ER -