"Contributions to Silting Theory"

code: PN-III-P4-ID-PCE-2020-0454; contract: 75/04.01.2021

January 2021-December 2023.

Financed by

Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii ,

4. Research visits, conferences

The main aim is to study (co)silting objects which can be associated to some categories, as module categories over some particular rings, Grothendieck or triangulated categories.

(I) Contributions to silting theory. The main topics will be the following:

(A) Silting and cosilting complexes in the derived categories. Structures related to these mathematical objects.

(B) The transfer of the (co)silting properties via functors.

(II) Special classes and objects. The topics are the following:

(A) Approximations and definable classes. We will study preenveloping and precovering classes induced by (co)silting objects.

(B) Pure-injective objects in Grothendieck and triangulated categories. We will try to use some triangulated versions for the classical notion of p-functor in order to obtain new information about the class of pure-injective objects.

(S1) Silting objects in module theory (silting, cosilting and t-tilting modules)

(S2) Silting objects in triangulated categories

(S3) Splitting properties and the structure of (pure) projective and (pure) injective modules.

(S4) Identities in rings and approximations.

1. S. Breaz: On a theorem of Stelzer for self-small mixed groups. To appear in

2. S. Breaz, Y. Zhou: When is every non central-unit a sum of two nilpotents?

3. Cs. Szanto, I. Szollosi: Ringel-Hall polynomials associated to a quiver of type $\tilde D_4$

1. S. Breaz, C.-G. Modoi: Migration of silting objects via adjoint pairs

2. S. Breaz, F. Pop: On extriangulated categories

3. S. Breaz, T. Brzezi\'nski, B. Rybo{\l}owicz, P. Saracco: Heaps of modules. First properties and applications

1. S. Breaz: Homological Methods in Representation Theory, A conference in honour of Lidia Angeleri Hugel, October 3 - 8, 2021; Fraueninsel (Chiemsee), Abtei Frauenworth, Germany. Talk:

2. C.-G. Modoi: Homological Methods in Representation Theory, A conference in honour of Lidia Angeleri Hugel, October 3 - 8, 2021; Fraueninsel (Chiemsee), Abtei Frauenworth, Germany.

*e-mail:*

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Simion Breaz

Babes-Bolyai University

Faculty of Mathematics and
Computer Science

Str. Mihail Kogalniceanu nr.
1

RO-400084 Cluj-Napoca

Romania