Cleaving functors and controlled wild algebras (Q1602680)

Let \(K\) be an algebraically closed field. Cleaving functors between module categories were introduced by \textit{R. Bautista, P. Gabriel, A. V. Rojter} and \textit{L. Salmerón} [Invent. Math. 81, 217-285 (1985; Zbl 0575.16012)] as elementary tools for showing that certain \(K\)-algebras \(R\) are of finite representation type. In the paper, the notion is extended to functor categories and they are used in the study of controlled wildness. In particular, it is proved that a finite dimensional \(K\)-algebra \(R\) is controlled wild if there is an indecomposable projective \(R\)-module with a Loewy factor having a homogeneous direct summand which is of length at least three. A new proof of \textit{Y. Han}'s covering criterion is also presented [see Proc. Lond. Math. Soc., III. Ser. 83, No. 2, 279-298 (2001; see the following review Zbl 1019.16007)].