Tensor products of higher almost split sequences in subcategories
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1151-1174.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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).
DOI : 10.21136/CMJ.2023.0432-22
Classification : 16D90, 16G10, 16G70
Keywords: $n$-representation finite algebra; higher almost split sequence; tensor product; mapping cone
@article{10_21136_CMJ_2023_0432_22,
     author = {Lu, Xiaojian and Luo, Deren},
     title = {Tensor products of higher almost split sequences in subcategories},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1151--1174},
     publisher = {mathdoc},
     volume = {73},
     number = {4},
     year = {2023},
     doi = {10.21136/CMJ.2023.0432-22},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0432-22/}
}
TY  - JOUR
AU  - Lu, Xiaojian
AU  - Luo, Deren
TI  - Tensor products of higher almost split sequences in subcategories
JO  - Czechoslovak Mathematical Journal
PY  - 2023
SP  - 1151
EP  - 1174
VL  - 73
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0432-22/
DO  - 10.21136/CMJ.2023.0432-22
LA  - en
ID  - 10_21136_CMJ_2023_0432_22
ER  - 
%0 Journal Article
%A Lu, Xiaojian
%A Luo, Deren
%T Tensor products of higher almost split sequences in subcategories
%J Czechoslovak Mathematical Journal
%D 2023
%P 1151-1174
%V 73
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0432-22/
%R 10.21136/CMJ.2023.0432-22
%G en
%F 10_21136_CMJ_2023_0432_22
Lu, Xiaojian; Luo, Deren. Tensor products of higher almost split sequences in subcategories. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1151-1174. doi : 10.21136/CMJ.2023.0432-22. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0432-22/

Cité par Sources :