A note on preprojective partitions over hereditary artin algebras
G Todorov - Proceedings of the American Mathematical Society, 1982 - ams.org
Proceedings of the American Mathematical Society, 1982•ams.org
If $\Lambda $ is an artin algebra there is a partition of $\operatorname {ind}\Lambda $, the
category of indecomposable finitely generated $\Lambda $-modules, $\operatorname
{ind}\Lambda={\cup _ {i\geqslant 0}}{\underline {\underline {P}} _i} $, called the preprojective
partition. We show that $\underline {\underline {P}} _i $ can be easily constructed for
hereditary artin algebras, if $\underline {\underline {P}} _ {i-1} $ is known: $ A $ is in
$\underline {\underline {P}} _i $ if and only if $ A $ is not in $\underline {\underline {P}} _ {i-1} …
category of indecomposable finitely generated $\Lambda $-modules, $\operatorname
{ind}\Lambda={\cup _ {i\geqslant 0}}{\underline {\underline {P}} _i} $, called the preprojective
partition. We show that $\underline {\underline {P}} _i $ can be easily constructed for
hereditary artin algebras, if $\underline {\underline {P}} _ {i-1} $ is known: $ A $ is in
$\underline {\underline {P}} _i $ if and only if $ A $ is not in $\underline {\underline {P}} _ {i-1} …
Abstract
If is an artin algebra there is a partition of , the category of indecomposable finitely generated -modules, , called the preprojective partition. We show that can be easily constructed for hereditary artin algebras, if is known: is in if and only if is not in and there is an irreducible map , where is in . References
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