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

100%

Dowbor P.

Colloquium Mathematicum

2000

tom 83

nr 2

231-265

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).

Hochschild Cohomology of skew group rings and invariants

75%

Marcos E., Martínez-Villa R., Martins M.

Open Mathematics

2004

tom 2

nr 2

177-190

Let A be a k-algebra and G be a group acting on A. We show that G also acts on the Hochschild cohomology algebra HH ⊙ (A) and that there is a monomorphism of rings HH ⊙ (A) G→HH ⊙ (A[G]). That allows us to show the existence of a monomorphism from HH ⊙ (Ã) G into HH ⊙ (A), where Ã is a Galois covering with group G.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Open Mathematics

1 Dowbor P.

1 Marcos E.

1 Martins M.

1 Martínez-Villa R.

1 2004

1 2000

Wyniki wyszukiwania

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

Hochschild Cohomology of skew group rings and invariants