Cokernels of the Cartan matrix and stratifying systems

Autor(es)

Marcos, Eduardo N. ^[1] ; Mendoza, Octavio ^[2] ; Saenz, Corina ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: COMMUNICATIONS IN ALGEBRA; v. 47, n. 8, p. 3076-3093, AUG 8 2019.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 14/09310-5 - Estruturas algébricas e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Temático