Algebra seminar
Henrik Holm (IMF, Univ. Kopenhagen): Minimal semi-injective models in categories of quiver representations
Abstract: It is a classic result that every module has an minimal injective resolution. More generally, every complex of modules, M, has a minimal semi-injective (or DG-injective) model; that is, there exists a quasi-isomorphism M -> I where I is a minimal semi-injective complex. The existence of such models can be found in works of Avramov-Foxby-Halperin (unpublished) and Garcia Rozas (1999). A (chain) complex can be viewed as a representation of the quiver ... -> 1 -> 0 -> -1 -> ... with the relations that any two consecutive arrows compose to zero. It is possible to extend the notions of "quasi-isomorphism", "minimality", and "semi-injectivity" to representations of (certain) other quivers with relations; for example, to differential modules, which are representations of the Jordan quiver with the relation that the square of the loop is zero. We will explain these notions and prove the existence of minimal semi-injective models in this more general context. As an application, we generalize a result by Ringel and Zhang on Gorenstein injective differential modules. The talk is based on joint work with Peter Jørgensen (Aarhus University).
April 27 - TBA
The Algebra Seminar was founded by Vladimir Korinek in the early 1950's and continued by Karel Drbohlav until 1981. The seminar resumed its activities in 1990 under the guidance of Jaroslav Jezek and Tomas Kepka. Since 1994, the seminar is headed by Jan Trlifaj.
Presently, the seminar is supported by GACR. It serves primarily as a platform for presentation of recent research of the visitors to the Department of Algebra as well as members of the Department and their students.
