# Properties of G-atoms and full Galois covering reduction to stabilizers

Colloquium Mathematicae (2000)

- Volume: 83, Issue: 2, page 231-265
- ISSN: 0010-1354

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topDowbor, Piotr. "Properties of G-atoms and full Galois covering reduction to stabilizers." Colloquium Mathematicae 83.2 (2000): 231-265. <http://eudml.org/doc/210784>.

@article{Dowbor2000,

abstract = {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).},

author = {Dowbor, Piotr},

journal = {Colloquium Mathematicae},

keywords = {Galois covering; tame; locally finite-dimensional module; Galois coverings; atoms; stabilizers; locally finite dimensional modules; categories of modules; infinite representation type},

language = {eng},

number = {2},

pages = {231-265},

title = {Properties of G-atoms and full Galois covering reduction to stabilizers},

url = {http://eudml.org/doc/210784},

volume = {83},

year = {2000},

}

TY - JOUR

AU - Dowbor, Piotr

TI - Properties of G-atoms and full Galois covering reduction to stabilizers

JO - Colloquium Mathematicae

PY - 2000

VL - 83

IS - 2

SP - 231

EP - 265

AB - 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).

LA - eng

KW - Galois covering; tame; locally finite-dimensional module; Galois coverings; atoms; stabilizers; locally finite dimensional modules; categories of modules; infinite representation type

UR - http://eudml.org/doc/210784

ER -

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