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SUMMARY:Periodicity for finite-dimensional selfinjective algebras - Karin 
 Erdmann (University of Oxford)
DTSTART:20170328T103000Z
DTEND:20170328T113000Z
UID:TALK71665@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:&nbsp\;We give  a survey on finite-dimensional selfinjective a
 lgebras which are periodic as bimodules\, with respect to syzygies\, and h
 ence are stably Calabi-Yau. These include preprojective algebras of Dynkin
  types ADE and  deformations\, as well a class of algebras which we call  
 mesh algebras  of generalized Dynkin type. There is also a classification 
 of the  selfinjective algebras of polynomial growth which are periodic.  F
 urthermore\, we introduce weighted surface algebras\, associated to triang
 ulations of compact surfaces\, they are tame and symmetric\, and have peri
 od 4 (they are 3-Calabi-Yau). They generalize Jacobian  algebras\, and als
 o blocks of finite groups with quaternion defect  groups. <br>  <span>&nbs
 p\;<br>In general\, for such an algebra\, all one-sided simple modules are
  periodic. One would like to know whether the converse holds: Given a fini
 te-dimensional selfinjective algebra A for which all  one-sided simple mod
 ules are periodic. It is known that then some syzygy  of A is isomorphic a
 s a bimodule to some twist of A by an automorphism.  It is open whether th
 en A must be periodic.</span>
LOCATION:Seminar Room 1\, Newton Institute
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