Aarhus University Seal

Finite Dimensional Differential Graded Algebras

Isambard Goodbody (University of Glasgow)
Wednesday 8 March 2023 14:15–15:15 Koll. G (1532-214)
Mathematics Seminar

A DGA is a chain complex with a compatible multiplication. In the case that the DGA is connective (concentrated in negative degrees) then these DGAs behave similarly to rings; they have the standard t-structure and their K-theory's are similar. Finite dimensional DGAs are a step towards studying nonconnective DGAs where many questions are still open. We say a DGA is finite dimensional if its underlying algebra is finite dimensional (not just its homology). This definition is not invariant under quasiisomorphism but the class of DGAs which are quasiisomorphic to fd ones still has some sensible properties. A result of Orlov says that if the underlying algebra of the fd DGA is semisimple then it is also semisimple as a DGA. In this sense the underlying algebra of the DGA determines some of the structure of the DGA. I'll present a result in same theme which builds on this result and mention some open problems I'm trying to apply it to.

Organised by: AarHomAlg
Contact: Karin M. Jacobsen Revised: 25.05.2023