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SUMMARY:Spherical Algebras and their Auslander—Yoneda Algebras [Obersemi
 nar Algebra und Darstellungstheorie]
DTSTART:20260924T140000Z
DTEND:20260924T160000Z
DTSTAMP:20260926T014400Z
UID:indico-event-1589@math-events.uni-bonn.de
DESCRIPTION:Speakers: Jan Thomm (Universität zu Köln)\, Marvin Plogmann 
 (Universität zu Köln)\n\nConsidering a hereditary algebra A and a module
  M over A\, Ext^n(M\,A)=0 unless n is equal to the projective dimension of
  M. Generalising this observation to algebras of finite global dimension\,
  Auslander and Bridger define a module M to be spherical if Ext^n(M\,A)=0 
 unless n is the projective dimension of M (or n=0). Motivated by this\, we
  call an algebra spherical if every indecomposable module is spherical. In
  this talk\, we will discuss structural properties of the module category 
 of a spherical algebra and give examples beyond the hereditary case. We wi
 ll then show that representation-finite bispherical algebras\, that is\, a
 lgebras that are spherical with respect to both left and right modules\, g
 ive rise to Auslander—Gorenstein algebras: If M is an additive generator
  of the module category\, then its Yoneda algebra Ext^*(M\,M) is Auslander
 —Gorenstein. In fact\, an appropriate version of this property character
 izes bispherical algebras\, even in the representation-infinite case. Fina
 lly\, we will discuss the Auslander—Reiten bijection for the Auslander
 —Gorenstein algebras arising in this way.\n\nhttps://math-events.uni-bon
 n.de/event/1589/
LOCATION:Endenicher Allee 60/1-008-Seminarraum (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1589/
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