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Keywords:
$n$-representation finite algebra; higher almost split sequence; tensor product; mapping cone
$n$-representation finite algebra; higher almost split sequence; tensor product; mapping cone
Summary:
We introduce the algebras satisfying the $(\mathcal B,n)$ condition. If $\Lambda $, $\Gamma $ are algebras satisfying the $(\mathcal B,n)$, $(\mathcal E,m)$ condition, respectively, we give a construction of $(m+n)$-almost split sequences in some subcategories $(\mathcal B\otimes \mathcal E)^{(i_0, j_0)}$ of $\mod (\Lambda \otimes \Gamma )$ by tensor products and mapping cones. Moreover, we prove that the tensor product algebra $\Lambda \otimes \Gamma $ satisfies the $((\mathcal B\otimes \mathcal E)^{(i_0, j_0)},n+m)$ condition for some integers $i_0$, $j_0$; this construction unifies and extends the work of A. Pasquali (2017), (2019).
References:
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