A construction of non-regularly orbicular modules for Galois coverings

Abstract

For a given finite dimensional k -algebra A which admits a presentation in the form R / G , where G is an infinite group of k -linear automorphisms of a locally bounded k -category R , a class of modules lying out of the image of the push-down functor associated with the Galois covering R → R / G , is studied. Namely, the problem of existence and construction of the so called non-regularly orbicular indecomposable R / G -modules is discussed. For a G -atom B (with a stabilizer G B ), whose endomorphism algebra has a suitable structure,a representation embedding Φ B ( f , s ) | : I n - s p r l ( s ) ( k G B ) → m o d ( R / G ) , which yields large families of non-regularly orbicular indecomposable R / G -modules,is constructed (Theorem 2.2). An important role in consideration is played by a result interpreting some class of R / G -modules in terms of Cohen-Macaulay modules over certain skew grup algebra (Theorem 3.3). Also, Theorems 4.5 and 5.4, adapting the generalized tensor product construction and Galois covering scheme, respectively, for Cohen-Macaulay modules context, are proved and intensively used.