A construction of non-regularly orbicular modules for Galois coverings

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  • DOWBOR Piotr
    Faculty of Mathematics and Computer Science Nicolaus Copernicus University

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  • A construction of non-regularly orbicular modules \\ for Galois coverings
  • construction of non regularly orbicular modules for Galois coverings

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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 \varPhiB(f, s)|:\isl(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.

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