Finite cycles of indecomposable modules

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dc.contributor.author Malicki, Piotr
dc.contributor.author Pena, Jose Antonio
dc.contributor.author Skowroński, Andrzej
dc.date.accessioned 2015-01-12T08:20:49Z
dc.date.available 2015-01-12T08:20:49Z
dc.date.issued 2013-11-25
dc.identifier.citation arXiv
dc.identifier.uri http://repozytorium.umk.pl/handle/item/2367
dc.description.abstract We solve a long standing open problem concerning the structure of finite cycles in the category $\mo A$ of finitely generated modules over an arbitrary artin algebra $A$, that is, the chains of homomorphisms $M_0 \buildrel {f_1}\over {\hbox to 6mm{\rightarrowfill}} M_1 \to \cdots \to M_{r-1} \buildrel {f_r}\over {\hbox to 6mm{\rightarrowfill}} M_r=M_0$ between indecomposable modules in $\mo A$ which do not belong to the infinite radical of $\mo A$. In particular, we describe completely the structure of an arbitrary module category $\mo A$ whose all cycles are finite. The main structural results of the paper allow to derive several interesting combinatorial and homological properties of indecomposable modules lying on finite cycles. For example, we prove that for all but finitely many isomorphism classes of indecomposable modules $M$ lying on finite cycles of a module category $\mo A$ the Euler characteristic of $M$ is well defined and nonnegative. Moreover, new types of examples illustrating the main results of the paper are presented.
dc.description.sponsorship This work was completed with the support of the research grant DEC-2011/02/A/ST1/00216 of the Polish National Science Center and the CIMAT Guanajuato, Mexico.
dc.language.iso eng
dc.rights info:eu-repo/semantics/openAccess
dc.subject Cycles of modules
dc.subject Generalized multicoil algebras
dc.subject Generalized double tilted algebras
dc.subject Auslander-Reiten quiver
dc.title Finite cycles of indecomposable modules
dc.type info:eu-repo/semantics/article

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