Upper recollements and triangle expansions
YQ Yin, N Gao - Acta Mathematica Sinica, English Series, 2016 - Springer
YQ Yin, N Gao
Acta Mathematica Sinica, English Series, 2016•SpringerBy using the stable t-structure induced by an adjoint pair, we extend several results
concerning recollements to upper (resp. lower) recollements. These include the fundamental
results of Parshall and Scott on comparisons of recollements, Wiedemann's result on the
global dimension and Happel's result on the finitistic dimension, occurring in a recollement
(D b (A′), D b (A), D b (A ″)) of bounded derived categories of Artin algebras. We introduce
and describe a triangle expansion of a triangulated category and illustrate it by examples.
concerning recollements to upper (resp. lower) recollements. These include the fundamental
results of Parshall and Scott on comparisons of recollements, Wiedemann's result on the
global dimension and Happel's result on the finitistic dimension, occurring in a recollement
(D b (A′), D b (A), D b (A ″)) of bounded derived categories of Artin algebras. We introduce
and describe a triangle expansion of a triangulated category and illustrate it by examples.
Abstract
By using the stable t-structure induced by an adjoint pair, we extend several results concerning recollements to upper (resp. lower) recollements. These include the fundamental results of Parshall and Scott on comparisons of recollements, Wiedemann’s result on the global dimension and Happel’s result on the finitistic dimension, occurring in a recollement (D b (A′),D b (A),D b (A″)) of bounded derived categories of Artin algebras. We introduce and describe a triangle expansion of a triangulated category and illustrate it by examples.
Springer
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