Tensor products of higher almost split sequences in subcategories

Xiaojian Lu; Deren Luo

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 4, page 1151-1174
  • ISSN: 0011-4642

Abstract

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We introduce the algebras satisfying the ( ℬ , n ) condition. If Λ , Γ are algebras satisfying the ( ℬ , n ) , ( ℰ , m ) condition, respectively, we give a construction of ( m + n ) -almost split sequences in some subcategories ( ℬ ⊗ ℰ ) ( i 0 , j 0 ) of mod ( Λ ⊗ Γ ) by tensor products and mapping cones. Moreover, we prove that the tensor product algebra Λ ⊗ Γ satisfies the ( ( ℬ ⊗ 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).

How to cite

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Lu, Xiaojian, and Luo, Deren. "Tensor products of higher almost split sequences in subcategories." Czechoslovak Mathematical Journal 73.4 (2023): 1151-1174. <http://eudml.org/doc/299462>.

@article{Lu2023,
abstract = {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).},
author = {Lu, Xiaojian, Luo, Deren},
journal = {Czechoslovak Mathematical Journal},
keywords = {$n$-representation finite algebra; higher almost split sequence; tensor product; mapping cone},
language = {eng},
number = {4},
pages = {1151-1174},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Tensor products of higher almost split sequences in subcategories},
url = {http://eudml.org/doc/299462},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Lu, Xiaojian
AU - Luo, Deren
TI - Tensor products of higher almost split sequences in subcategories
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 4
SP - 1151
EP - 1174
AB - 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).
LA - eng
KW - $n$-representation finite algebra; higher almost split sequence; tensor product; mapping cone
UR - http://eudml.org/doc/299462
ER -

References

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