Two classes of almost Galois coverings for algebras

Piotr Dowbor ¹   ; Adam Hajduk ¹

¹ Faculty of Mathematics and Computer Science Nicolaus Copernicus University 87-100 Toruń, Poland

Colloquium Mathematicum, Tome 127 (2012) no. 2, pp. 253-298

Résumé

We prove that for any representation-finite algebra $A$ (in fact, finite locally bounded $k$-category), the universal covering $F: \tilde{A}\to A$ is either a Galois covering or an almost Galois covering of integral type, and $F$ admits a degeneration to the standard Galois covering $\bar{F}: \tilde{A}\to \tilde{A}/G$, where $G=\Pi(\Gamma_A)$ is the fundamental group of $\Gamma_A$. It is shown that the class of almost Galois coverings $F:R\to R'$ of integral type, containing the series of examples from our earlier paper [Bol. Soc. Mat. Mexicana 17 (2011)], behaves much more regularly than usual with respect to the standard properties of the pair $(F_\lambda, F_\bullet)$ of adjoint functors associated to $F $.

Détail

DOI : 10.4064/cm127-2-8

Keywords: prove representation finite algebra finite locally bounded k category universal covering tilde either galois covering almost galois covering integral type admits degeneration standard galois covering bar tilde tilde where gamma fundamental group gamma shown class almost galois coverings integral type containing series examples earlier paper bol soc mat mexicana behaves much regularly usual respect standard properties pair lambda bullet adjoint functors associated