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Colloquium Mathematicum

2001 | 89 | 2 | 241-310
Tytuł artykułu

Non-orbicular modules for Galois coverings

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Języki publikacji
EN
Abstrakty
EN
Given a group G of k-linear automorphisms of a locally bounded k-category R, the problem of existence and construction of non-orbicular indecomposable R/G-modules is studied. For a suitable finite sequence B of G-atoms with a common stabilizer H, a representation embedding $Φ^{B} : Iₙ - spr(H) → mod(R/G)$, which yields large families of non-orbicular indecomposable R/G-modules, is constructed (Theorem 3.1). It is proved that if a G-atom B with infinite cyclic stabilizer admits a non-trivial left Kan extension B̃ with the same stabilizer, then usually the subcategory of non-orbicular indecomposables in $mod_{B̃,B}(R/G)$ is wild (Theorem 4.1, also 4.5). The analogous problem for the case of different stabilizers is discussed in Theorem 5.5. It is also shown that if R is tame then B̃ ≃ B for any infinite G-atom B with $End_{R}(B)/J(End_{R}(B)) ≃ k$ (Theorem 7.1). For this purpose the techniques of neighbourhoods (Theorem 7.2) and extension embeddings for matrix rings (Theorem 6.3) are developed.
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Kategorie tematyczne
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Rocznik
Tom
Numer
Strony
241-310
Opis fizyczny
Daty
wydano
2001
Twórcy
autor
• Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
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