Finite Dimensional DGAs

Isambard Goodbody (University of Glasgow)

Wednesday 26th April, 2023 16:00-17:00 Maths 311B


A DGA is a chain complex with a compatible multiplication. These appear in algebra and geometry as any derived category which is generated by a single object is equivalent to the derived category of a DGA. A finite dimensional DGA is one whose underlying chain complex is finite dimensional and so they generalise fd algebras. Orlov has constructed a radical filtration for fd DGAs and we use this to prove some properties reminiscent of fd algebras. One property is that the simples can detect modules with finite projective dimension; this gives a new characterisation of perfect DG-modules. Another is the projective-simple bijection; this fails to generalise fully due to the existence of phantoms. However we introduce a class of fd DGAs with an idempotent lifting property for which this does hold. Using this we can answer some open questions about Grothendieck groups and phantoms.


Add to your calendar

Download event information as iCalendar file (only this event)