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Recollements and Gorenstein algebras. (English) Zbl 1305.18050

Summary: Let \(A\), \(B\) and \(C\) be finite dimensional algebras. In this paper, we prove that if \(A\) is a Gorenstein algebra such that \(D^b(A)\) has a recollement relative to \(D^b(B)\) and \(D^b(C)\), then \(B\) and \(C\) are Gorenstein algebras.

MSC:

18E30 Derived categories, triangulated categories (MSC2010)
16G10 Representations of associative Artinian rings
18G15 Ext and Tor, generalizations, Künneth formula (category-theoretic aspects)
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