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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Cokernels of the Cartan matrix and stratifying systems

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Author(s):
Marcos, Eduardo N. [1] ; Mendoza, Octavio [2] ; Saenz, Corina [3]
Total Authors: 3
Affiliation:
[1] Univ Sao Paulo, Inst Matemat & Estadist, Sao Paulo - Brazil
[2] Univ Nacl Autonoma Mexico, Inst Matemat, Ciudad Univ, Mexico City, DF - Mexico
[3] Univ Nacl Autonoma Mexico, Dept Matemat, Fac Ciencias, Ciudad Univ, Mexico City, DF - Mexico
Total Affiliations: 3
Document type: Journal article
Source: COMMUNICATIONS IN ALGEBRA; v. 47, n. 8, p. 3076-3093, AUG 8 2019.
Web of Science Citations: 0
Abstract

We study the cokernel of the application given by the Cartan matrix C of a finite dimensional k-algebra This produces a finitely generated abelian group, the Cartan group which is invariant under derived equivalences. We are interested in the case when G is finite. For a standardly stratified algebra, it is shown that this group is always finite and some interesting connections with the standard modules are found. As a consequence, it is got that G can be seen as a measure of how far is a standardly stratified algebra to be quasi-hereditary. Finally, it is also shown that any finite abelian group can be realized as the Cartan group of some standardly stratified algebra. (AU)

FAPESP's process: 14/09310-5 - Algebraic structures and their representations
Grantee:Vyacheslav Futorny
Support Opportunities: Research Projects - Thematic Grants