Geodesic
Koszul and quasi-Koszul algebras obtained by tilting
R. M. Aquino 1   ; E. L. Green 2   ; E. N. Marcos 1
1 Departamento de Matemática Pura Instituto de Matemática e Estatistica da Universidade de São Paulo rua do Matão, 1010 05508-900 São Paulo, SP, Brazil
2 Mathematics Department Virginia Polytechnic Institute and State University Blacksburg, VA 24061-0123, USA
Colloquium Mathematicum, Tome 92 (2002) no. 2, pp. 197-224 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm92-2-5
Keywords: given finite dimensional algebra present sufficient conditions projective presentation algebra modulo its radical tilted algebra koszul algebra endomorphism ring tilting module quasi koszul algebra condition impose algebra has global dimension greater main techniques studying maps between direct summands tilting module applications given brenner butler tilted algebra simply connected only original algebra simply connected

R. M. Aquino  1   ; E. L. Green  2   ; E. N. Marcos  1

1 Departamento de Matemática Pura Instituto de Matemática e Estatistica da Universidade de São Paulo rua do Matão, 1010 05508-900 São Paulo, SP, Brazil
2 Mathematics Department Virginia Polytechnic Institute and State University Blacksburg, VA 24061-0123, USA 
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     title = {Koszul and {quasi-Koszul
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     journal = {Colloquium Mathematicum},
     pages = {197--224},
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R. M. Aquino; E. L. Green; E. N. Marcos. Koszul and quasi-Koszul
algebras obtained by tilting. Colloquium Mathematicum, Tome 92 (2002) no. 2, pp. 197-224. doi: 10.4064/cm92-2-5

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