Algebraický seminář
Jan Trlifaj (MFF UK): Title Finitistic dimensions, the Cummings construction, and tilting
Abstract: Finiteness of the right little finitistic dimension of a finite dimensional algebra A is known to be equivalent to the existence of a (possibly infinite dimensional) largest tilting right A-module T_f. We use this equivalence to interpret the recent results of Cummings concerning the asymmetry of left and right finitistic dimensions of particular triangular matrix algebras A' built from arbitrary basic finite dimensional algebras A. Our main result determines the structure of the largest tilting right A'-module T'_f in terms of the structure of T_f in case A has finite right global dimension or A is Iwanaga-Gorenstein (joint work with J.Šťovíček and M.Dubov).
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.
