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October, 2005 A construction of non-regularly orbicular modules for Galois coverings
J. Math. Soc. Japan 57(4): 1077-1127 (October, 2005). DOI: 10.2969/jmsj/1150287305


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.


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Piotr DOWBOR. "A construction of non-regularly orbicular modules for Galois coverings." J. Math. Soc. Japan 57 (4) 1077 - 1127, October, 2005.


Published: October, 2005
First available in Project Euclid: 14 June 2006

zbMATH: 1121.16013
MathSciNet: MR2183585
Digital Object Identifier: 10.2969/jmsj/1150287305

Primary: 16G60

Keywords: Cohen-Macaulay module , Galois covering , generalized tensor product

Rights: Copyright © 2005 Mathematical Society of Japan


Vol.57 • No. 4 • October, 2005
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