Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 57, Number 4 (2005), 1077-1127.
A construction of non-regularly orbicular modules for Galois coverings
For a given finite dimensional -algebra which admits a presentation in the form , where is an infinite group of -linear automorphisms of a locally bounded -category , a class of modules lying out of the image of the "push-down" functor associated with the Galois covering , is studied. Namely, the problem of existence and construction of the so called non-regularly orbicular indecomposable -modules is discussed. For a -atom (with a stabilizer ), whose endomorphism algebra has a suitable structure,a representation embedding , which yields large families of non-regularly orbicular indecomposable -modules,is constructed (Theorem 2.2). An important role in consideration is played by a result interpreting some class of -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.
J. Math. Soc. Japan, Volume 57, Number 4 (2005), 1077-1127.
First available in Project Euclid: 14 June 2006
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 16G60: Representation type (finite, tame, wild, etc.)
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