Mathematics – Representation Theory
Scientific paper
2011-01-20
Mathematics
Representation Theory
13 pages
Scientific paper
nspired by the work of J$\o$rgensen [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 $\m = \left(\begin{smallmatrix} A&M 0&B \end{smallmatrix}\right)$ with bimodule $_AM_B$. We construct an upper-symmetric abelian category recollement of $\m$-mod; and a symmetric triangulated category recollement of $\underline {\m\mbox{-}\mathcal Gproj}$ if $A$ and $B$ are Gorenstein and $_AM$ and $M_B$ are projective.
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