## Two classes of almost Galois coverings for algebras

### Volume 127 / 2012

Colloquium Mathematicum 127 (2012), 253-298
MSC: Primary 16G99; Secondary 16G60.
DOI: 10.4064/cm127-2-8

#### Abstract

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 $.