»ã±¨±êÌâ (Title)£ºRelation between the Nakayama automorphisms and modular derivations under filtered deformations£¨Nakayama×Ôͬ¹¹ºÍÂËÐαäϵÄÄ£µ¼×ÓÖ®¼äµÄ¹Øϵ£©

»ã±¨ÈË (Speaker)£ºÎâȪˮ ½ÌÊÚ£¨¸´µ©´óѧ£©

»ã±¨¹¦·ò (Time)£º2024Äê10ÔÂ22ÈÕ(Öܶþ) 16:10-17:10

»ã±¨µØÖ· (Place)£º У±¾²¿D109

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Abstract£º

For any positively filtered algebra, the property of skew Calabi-Yau or having Van den Bergh duality can be lifted as usual, but not for Calabi-Yau property. Calabi-Yau property often emerges form the deformation of unimodular Poisson structure. Suppose A is a filtered algebra such that the associated graded algebra gr(A) is commutative Calabi-Yau. Then gr(A) has a canonical Poisson structure with a modular derivation. We describe the connection between the Nakayama automorphism of A and the modular derivation of gr(A) by using homological determinants as a bridge. In particular, it is proved that A is Calabi-Yau if and only if gr(A) is unimodular as Poisson algebra under some mild assumptions. As an application, we derive that the ring of differential operators over a smooth variety is Calabi-Yau. Some other applications will also be given in the talk.