A construction of non-regularly orbicular modules for Galois coverings

摘要

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-spr ι(s)(kG_B) → mod(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.