Koszul and quasi-Koszul algebras obtained by tilting

• Autorzy: R. M. Aquino , E. L. Green , E. N. Marcos
• Języki publikacji: EN

Abstrakty

EN

Given a finite-dimensional algebra, we present sufficient conditions on the projective presentation of the algebra modulo its radical for a tilted algebra to be a Koszul algebra and for the endomorphism ring of a tilting module to be a quasi-Koszul algebra. One condition we impose is that the algebra has global dimension no greater than 2. One of the main techniques is studying maps between the direct summands of the tilting module. Some applications are given. We also show that a Brenner-Butler tilted algebra is simply connected if and only if the original algebra is simply connected.

Kategorie tematyczne

• 16S34: Group rings , Laurent polynomial rings
• 16S50: Endomorphism rings; matrix rings
• 16W50: Graded rings and modules

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2002
• Tom: 92
• Numer: 2
• Strony: 197-224

Daty

wydano

2002

Twórcy

autor

R. M. Aquino

• Departamento de Matemática Pura, Instituto de Matemática e Estatistica, da Universidade de São Paulo, rua do Matão, 1010, 05508-900 São Paulo, SP, Brazil

autor

E. L. Green

• Mathematics Department, Virginia Polytechnic Institute, and State University, Blacksburg, VA 24061-0123, USA

autor

E. N. Marcos

• Departamento de Matemática Pura, Instituto de Matemática e Estatistica, da Universidade de São Paulo, rua do Matão, 1010, 05508-900 São Paulo, SP, Brazil

Identyfikatory

DOI

10.4064/cm92-2-5