Abstract: If A is a finite dimensional algebra, and D(A) the unbounded
derived category of the full module category Mod-A, then it is
straightforward to see that D(A) is generated (as a "localizing
subcategory") by the indecomposable projectives, and by the simple
modules. It is not so obvious whether it is generated by the
indecomposable injectives. In 2001, Keller gave a talk in which he
remarked that"injectives generate" would imply several of the well-known
homological conjectures, such as the Nunke condition and hence the
generalized Nakayama
conjecture, and asked if there was any relation to the finitistic
dimension conjecture. I'll show that an algebra that satisfies "injectives
generate" also satisfies the finitistic dimension conjecture and discuss
some examples. I'll present things in a fairly concrete way, so most of
the talk won't assume much knowledge of derived categories.
Seminar series
Date
Thu, 24 Aug 2017
Time
15:00 -
16:00
Location
L6
Speaker
Jeremy Rickard
Organisation
Bristol University