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Symposium on Homological Algebra

Wednesday 23 November 2022 14:15–17:00 Aud. G1 (1532-116)

14:15-15:00: Johanne Haugland

Extension closure by indecomposables

Extension-closed subcategories of abelian categories form an important class of subcategories in representation theory. These subcategories carry a natural exact structure, and any small exact category can be seen to arise in this way. For nice classes of algebras, extensions with indecomposable end-terms can be realized geometrically as intersections of curves. In this talk, we show that when checking if a subcategory is extension-closed, it is enough to consider extensions by indecomposables. As an application, we aim to geometrically characterize extension-closed subcategories of the module category over a gentle algebra. The talk is based on joint work in progress with Sondre Kvamme and Steffen Oppermann.

15:15-16:00: Anders Sten Kortegård

Derived equivalences of self-injective 2-Calabi-Yau tilted algebras

In a $k$-linear Frobenius category $\mathscr{E}$ with a “nice” associated stable category $\mathscr{C}$, “good” maximal rigid objects have derived equivalent endomorphism algebras over $\mathscr{E}$. One may ask if the endomorphism algebras of the same objects over $\mathscr{C}$ also will be derived equivalent. We give a criteria for this being the case, and describe a two-sided tilting complex inducing this derived equivalence.

16:15-17:00: Matt Booth

Global Koszul duality

Koszul duality (a.k.a. bar-cobar duality) is a duality theory which gives an equivalence between the categories of augmented differential graded algebras, and coaugmented conilpotent differential graded coalgebras, when both are considered up to an appropriate notion of weak equivalence. More precisely, both categories admit model structures making the bar-cobar adjunction into a Quillen equivalence. Koszul duality (and variants, especially the commutative/Lie duality) pervades various different areas of mathematics, including rational homotopy theory and derived deformation theory. In this talk, I'll outline an extension of the above theory to the setting where one works with coalgebras that are no longer conilpotent (this is the `global' setting from the title). This is a report on work in progress joint with Andrey Lazarev.

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