Pullback and dimensional algebras representation

• Grant number: 12/50485-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2012
• End date: July 09, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Flavio Ulhoa Coelho
• Grantee: Heily Wagner
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This project aims the natural continuation of the study initiated by the candidate on her doctorate, which has generated two articles which are now in the process of finalization. They will be submitted for publication in specialized journals in the forthcoming months. This study concentrates on two main issues: pullback of finite dimensional algebras over a field, especially in relation to homological properties; and the representation dimension of Artin algebras, especially the study of new techniques involving sub-categories of the category of modules order to determining the representation dimension of some classes of algebras and also of the pullback of algebras. To exemplify the kind of result we want, we will mention some results already obtained by the candidate. The first shows that the pullback of hereditary algebras is a tilted algebra when considering a specific pullback, called pullback Dynkin oriented. We would like to obtain similar results involving other types of pullback and other classes of algebras, such as shod, weakly shod, laura, sided supported, etc. In relation to the representation dimension, the work of the candidate relates the representation dimension of an algebra with special subcategories of the category of modules. Put simply, if we divide the category of indecomposable modules into pieces with certain characteristics, we can calculate the representation dimension of this algebra by calculating this invariant of algebras associated to each piece. This technique allowed us to calculate the representation dimension of the ada algebras, for instance. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

ASSEM, IBRAHIM; COELHO, FLAVIO U.; WAGNER, HEILY. On subcategories closed under predecessors and the representation dimension. Journal of Algebra, v. 418, p. 174-196, NOV 15 2014. (12/50485-8)