Geodesic
Properties of G-atoms and full Galois covering reduction to stabilizers
Colloquium Mathematicum, Tome 83 (2000) no. 2, pp. 231-265 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

Given a group G of k-linear automorphisms of a locally bounded k-category R it is proved that the endomorphism algebra $End_R (B)$ of a G-atom B is a local semiprimary ring (Theorem 2.9); consequently, the injective $End_R (B)$-module $(End_R (B))^*$ is indecomposable (Corollary 3.1) and the socle of the tensor product functor $- ⊗_R B^*$ is simple (Theorem 4.4). The problem when the Galois covering reduction to stabilizers with respect to a set U of periodic G-atoms (defined by the functors $Φ^U: \coprod_{B ∈ U} mod kG_B → mod(R/G)$ and $Ψ^U: mod(R/G) → \prod_{B ∈ U} mod kG_B$)is full (resp. strictly full) is studied (see Theorems A, B and 6.3).
DOI : 10.4064/cm-83-2-231-265
Keywords: Galois covering, tame, locally finite-dimensional module

Piotr Dowbor 1

1 
@article{10_4064_cm_83_2_231_265,
     author = {Piotr Dowbor},
     title = {Properties of {G-atoms} and full {Galois} covering reduction to stabilizers},
     journal = {Colloquium Mathematicum},
     pages = {231--265},
     year = {2000},
     volume = {83},
     number = {2},
     doi = {10.4064/cm-83-2-231-265},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-83-2-231-265/}
}
TY  - JOUR
AU  - Piotr Dowbor
TI  - Properties of G-atoms and full Galois covering reduction to stabilizers
JO  - Colloquium Mathematicum
PY  - 2000
SP  - 231
EP  - 265
VL  - 83
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm-83-2-231-265/
DO  - 10.4064/cm-83-2-231-265
LA  - en
ID  - 10_4064_cm_83_2_231_265
ER  - 
%0 Journal Article
%A Piotr Dowbor
%T Properties of G-atoms and full Galois covering reduction to stabilizers
%J Colloquium Mathematicum
%D 2000
%P 231-265
%V 83
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/cm-83-2-231-265/
%R 10.4064/cm-83-2-231-265
%G en
%F 10_4064_cm_83_2_231_265
Piotr Dowbor. Properties of G-atoms and full Galois covering reduction to stabilizers. Colloquium Mathematicum, Tome 83 (2000) no. 2, pp. 231-265. doi: 10.4064/cm-83-2-231-265

Cité par Sources :