On Frobenius algebras

By Takayoshi Wakamatsu. 2003

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Extensions of a dualizing complex by its ring: commutative versions of a conjecture of Tachikawa (2002, background): “It has generated a significant body of research and has led to the study of several variants and to the formulation of equivalent forms, see Yamagata[26] for a general presentation of the subject.”
Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras (2014, methodology): “robenius algebra in certain cases. Since we do not yet have any assumptions to ensure that this algebra is ﬁnite dimensional, we rely on the inﬁnite dimensional generalization of Frobenius algebra in [Ja]. Following Jans, a k-algebra Ais Frobenius if there is an associative nondegenerate bilinear pa”
Periodic Algebras which are Almost Koszul (2002, methodology): “The following corollary shows that β is a Nakayama automorphism of B in the sense defined by Yamagata in [29].”
Algebras that satisfy Auslander’s condition on vanishing of cohomology (2008, background): “It is proved in [40,42] that the Nakayama Conjecture holds if and only if both Tachikawa Conjectures hold.”