TY - JOUR
ID - 110817
TI - Homotopy Category of Cotorsion Flat Representations of Quivers
JO - Mathematics Interdisciplinary Research
JA - MIR
LA - en
SN - 2538-3639
AU - Eshraghi, Hossein
AD - Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. Iran
Y1 - 2020
PY - 2020
VL - 5
IS - 4
SP - 279
EP - 294
KW - Homotopy category
KW - Cotorsion pair
KW - compact object
KW - Representations of a Quiver
DO - 10.22052/mir.2020.237654.1219
N2 - Recently in [10], it was proved that over any ring R, there exists a complete cotorsion pair (Kp(Flat-R); K(dg-CotF-R)) in K(Flat-R), the homotopy category of complexes of flat R-modules, where Kp(Flat-R) and K(dg-CotF-R) are the homotopy categories raised by flat (or pure) and dgcotorsion complexes of flat R-modules, respectively. This paper aims at recognition of a parallel cotorsion pair in K(Flat-Q), the homotopy category of flat representation of certain quivers Q, where Q may also be infinite. The importance of this result lies in the fact that this homotopy categories do not necessarily raise from the category of modules over some ring. In the other part of this paper, we give a classification of compact objects in K(dg-CotF-Q), the homotopy category of dg-cotorsion complexes of flat representations of certain Q, in terms of the corresponding vertex-complexes
UR - https://mir.kashanu.ac.ir/article_110817.html
L1 - https://mir.kashanu.ac.ir/article_110817_adb30153d64d87e593e5843f8eb85101.pdf
ER -