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Auslander-Gorenstein algebras from Serre-formal algebras via replication. (arXiv:1707.03996v1 [math.RT])
来源于:arXiv
We introduce a new family of algebras, called Serre-formal algebras. They are
Iwanaga-Gorenstein algebras for which applying any power of the Serre functor
on any indecomposable projective module, the result remains a stalk complex.
Typical examples are given by (higher) hereditary algebras and self-injective
algebras; it turns out that other interesting algebras such as (higher)
canonical algebras are also Serre-formal.
Starting from a Serre-formal algebra, we consider a series of algebras -
called the replicated algebras - given by certain subquotients of its
repetitive algebra. We calculate the self-injective dimension and dominant
dimension of all such replicated algebras and determine which of them are
minimal Auslander-Gorenstein, i.e. when the two dimensions are finite and equal
to each other. In particular, we show that there exist infinitely many minimal
Auslander-Gorenstien algebras in such a series if, and only if, the
Serre-formal algebra is twisted fractionally Calabi-Yau. 查看全文>>