English

Symmetric recollements induced by bimodule extensions

Representation Theory 2011-01-21 v1

Abstract

nspired by the work of J\o\orgensen [J], we define a (upper-, lower-) symmetric recollements; and give a one-one correspondence between the equivalent classes of the upper-symmetric recollements and one of the lower-symmetric recollements, of a triangulated category. Let \m=(AM0B)\m = \left(\begin{smallmatrix} A&M 0&B \end{smallmatrix}\right) with bimodule AMB_AM_B. We construct an upper-symmetric abelian category recollement of \m\m-mod; and a symmetric triangulated category recollement of \m\mboxGproj\underline {\m\mbox{-}\mathcal Gproj} if AA and BB are Gorenstein and AM_AM and MBM_B are projective.

Keywords

Cite

@article{arxiv.1101.3871,
  title  = {Symmetric recollements induced by bimodule extensions},
  author = {Pu Zhang},
  journal= {arXiv preprint arXiv:1101.3871},
  year   = {2011}
}

Comments

13 pages

R2 v1 2026-06-21T17:14:26.831Z