Tensor products of higher almost split sequences in subcategories

Lu, Xiaojian ; Luo, Deren

Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1151-1174

Abstract (VO)

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).

Détail

DOI : 10.21136/CMJ.2023.0432-22

Classification : 16D90, 16G10, 16G70
Keywords: $n$-representation finite algebra; higher almost split sequence; tensor product; mapping cone

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