Abstract
This paper is devoted to studying the recollement of the categories of finitely generated modules over finite dimensional algebras. We prove that for algebras A, B and C, if A-mod admits a recollement relative to B-mod and C-mod, then A[R]-mod admits a recollement relative to B[S]-mod and C-mod, where A[R] and B[S] are the one-point extensions of A by R and of B by S.
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References
Grothendieck A. Groups and classes des categories abeliennes et trianguliers complexe parfaits. In: Lecture Notes in Mathematics Vol. 589, New York: Springer-Verlag, 1977, 351–371
Beilinson A A, Bernstein J, Deligne P. Faisceaux pervers. In: Analyse et topologie sur les espaces singuliers. Asterisque, Vol. 100, Paris: Soc Math de France, 1982, 1–172
Parshall B, Scott L. Derived categories, quasi-hereditary algebras and algebraic groups. Carlton University Mathematical Notes, Vol. 3, 1988, 1–104
Beligiannis A, Reiten I. Homological and homotopical aspects of torsion theories. Mem Amer Math Soc, 188 (2007)
Franjou V, Pirashvili T. Comparison of abelian categories recollement. Doc Math, 9: 41–56 (2004)
MacPherson R, Vilonen K. Elementary construction of perverse sheaves. Invent Math, 84: 403–436 (1986)
Ringel C M. Tame algebras and integral quadratic forms. Lecture Notes in Mathematics Vol. 1099, Berlin-Heidelberg-New York: Springer, 1984
Hilton P J, Stammbach U. A course in homological algebra, 2nd ed. New York: Springer-Verlag, 2003
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This work was supported by the National Natural Science Foundation of China (Grant No. 10671161)
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Lin, Y., Lin, Z. One-point extension and recollement. Sci. China Ser. A-Math. 51, 376–382 (2008). https://doi.org/10.1007/s11425-008-0032-0
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DOI: https://doi.org/10.1007/s11425-008-0032-0