Koszul and quasi-Koszul algebras obtained by tilting

R. M. Aquino, E. L. Green, and E. N. Marcos. "Koszul and quasi-Koszul algebras obtained by tilting." Colloquium Mathematicae 92.2 (2002): 197-224. <http://eudml.org/doc/284811>.

@article{R2002,
abstract = {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.},
author = {R. M. Aquino, E. L. Green, E. N. Marcos},
journal = {Colloquium Mathematicae},
keywords = {Koszul algebras; quasi-Koszul algebras; tilting theory; tilted algebras; endomorphism algebras; tilting modules},
language = {eng},
number = {2},
pages = {197-224},
title = {Koszul and quasi-Koszul algebras obtained by tilting},
url = {http://eudml.org/doc/284811},
volume = {92},
year = {2002},
}

TY - JOUR
AU - R. M. Aquino
AU - E. L. Green
AU - E. N. Marcos
TI - Koszul and quasi-Koszul algebras obtained by tilting
JO - Colloquium Mathematicae
PY - 2002
VL - 92
IS - 2
SP - 197
EP - 224
AB - 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.
LA - eng
KW - Koszul algebras; quasi-Koszul algebras; tilting theory; tilted algebras; endomorphism algebras; tilting modules
UR - http://eudml.org/doc/284811
ER -