## Journal of the Mathematical Society of Japan

### A construction of non-regularly orbicular modules for Galois coverings

Piotr DOWBOR

#### 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 $R\to R/G$, 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 $\Phi^{B(f,s)}{}_{|}:I_n-\mathrm{spr}_{l(s)}(kG_B)\to \mathrm{mod}(R/G)$, 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.

#### Article information

Source
J. Math. Soc. Japan, Volume 57, Number 4 (2005), 1077-1127.

Dates
First available in Project Euclid: 14 June 2006

https://projecteuclid.org/euclid.jmsj/1150287305

Digital Object Identifier
doi:10.2969/jmsj/1150287305

Mathematical Reviews number (MathSciNet)
MR2183585

Zentralblatt MATH identifier
1121.16013

Subjects
Primary: 16G60: Representation type (finite, tame, wild, etc.)

#### Citation

DOWBOR, Piotr. A construction of non-regularly orbicular modules for Galois coverings. J. Math. Soc. Japan 57 (2005), no. 4, 1077--1127. doi:10.2969/jmsj/1150287305. https://projecteuclid.org/euclid.jmsj/1150287305

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