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# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Koszul and quasi-Koszul algebras obtained by tilting

### Tom 92 / 2002

Colloquium Mathematicum 92 (2002), 197-224 MSC: Primary 16S34; Secondary 16S50, 16W50. DOI: 10.4064/cm92-2-5

#### Streszczenie

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.

#### Autorzy

• R. M. AquinoDepartamento de Matemática Pura
Instituto de Matemática e Estatistica
rua do Matão, 1010
05508-900 São Paulo, SP, Brazil
e-mail
• E. L. GreenMathematics Department
Virginia Polytechnic Institute
and State University
Blacksburg, VA 24061-0123, USA
e-mail
• E. N. MarcosDepartamento de Matemática Pura
Instituto de Matemática e Estatistica