Department of Mathematics, Faculty of Mathematics and Computer Science "Babes-Bolyai" University, Cluj-Napoca


Research Project

"Contributions to Silting Theory"

(Romanian version)
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 , UEFISCDI

1. Team

2. Abstract

3. Results

4. Research visits, conferences

Contact



Team:

Simion Breaz
Andrei Marcus
Tudor Micu
George Ciprian Modoi
Cosmin Pelea
Flaviu Pop
Szanto Csaba
Abstract:
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.
A) SCIENTIFIC OBJECTIVES:
(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.


B) ADMINISTRATIVE OBJECTIVES: 1.Completion of the research infrastructure by assuring the bibliographical background (books, journals) and the material background of the research (computers, office consumables etc.) 2.Improving the level of knowledge of the team members and other young researchers and students.

C) Research seminars:
 (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.

Summary of our activities in the year: 2021

Reports:
(A) Papers submmited or accepted for publication
1. S. Breaz: On a theorem of Stelzer for self-small mixed groups. To appear in Mediterranean Journal of Mathematics

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

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

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





Visits, conferences, workshops
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: Transfer of homological properties along some canonical functors

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.




Contact

e-mail:
    user: bodo server: @math.ubbcluj.ro
    name: ssbreaz server: gmail.com
fax:
    +40 264 691906
mail:
    Simion Breaz
    Babes-Bolyai University
    Faculty of Mathematics and Computer Science
    Str. Mihail Kogalniceanu nr. 1
    RO-400084 Cluj-Napoca
    Romania