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SUMMARY:Preprojective algebras and Calabi-Yau algebras - Osamu Iyama (Nago
 ya University)
DTSTART:20170328T090000Z
DTEND:20170328T100000Z
UID:TALK71664@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Preprojective algebras are one of the central objects in repre
 sentation theory.&nbsp\;The preprojective algebra of a quiver Q is a grade
 d algebra whose degree zero part is&nbsp\;the path algebra kQ of Q\, and e
 ach degree i part gives a distinguished class of&nbsp\;representations of 
 Q\, called the preprojective modules. It categorifies the Coxeter groups&n
 bsp\;as reflection functors\, and their structure depends on the trichotom
 y of quivers: Dynkin\,&nbsp\;extended Dynkin\, and wild.&nbsp\;From homolo
 gical algebra point of view\, the algebra kQ is hereditary (i.e. global di
 mension&nbsp\;at most one)\, and its preprojective algebra is 2-Calabi-Yau
 .<br>In this talk\, I will discuss the higher preprojective algebras P of 
 algebras A of finite global&nbsp\;dimension d. When d=2\, then P is the Ja
 cobi algebra of a certain quiver with potential.&nbsp\;When A is a d-hered
 itary algebra\, a certain distinguished class of algebras of global&nbsp\;
 dimension d\, then its higher preprojective algebra is (d+1)-Calabi-Yau.&n
 bsp\;I will explain results and examples of higher preprojective algebras 
 based on joint works&nbsp\;with Herschend and Oppermann. If time permits\,
  I will explain a joint work with Amiot&nbsp\;and Reiten on algebraic McKa
 y correspondence for higher preprojective algebras.
LOCATION:Seminar Room 1\, Newton Institute
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