Recent developments around partial actions
M Dokuchaev - São Paulo Journal of Mathematical Sciences, 2019 - Springer
We give an overview of publications on partial actions and related concepts, paying main
attention to some recent developments on diverse aspects of the theory, such as partial …
attention to some recent developments on diverse aspects of the theory, such as partial …
Epsilon-strongly groupoid-graded rings, the Picard inverse category and cohomology
We introduce the class of partially invertible modules and show that it is an inverse category
which we call the Picard inverse category. We use this category to generalize the classical …
which we call the Picard inverse category. We use this category to generalize the classical …
Partial generalized crossed products and a seven-term exact sequence
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Partial generalized crossed products, Brauer groups and a comparison of seven-term exact sequences
M Dokuchaev, H Pinedo, I Rocha - arXiv preprint arXiv:2411.00494, 2024 - arxiv.org
Given a unital partial action $\alpha $ of a group $ G $ on a commutative ring $ R $ we
denote by ${\bf PicS} _ {R^{\alpha}}(R) $ the Picard monoid of the isomorphism classes of …
denote by ${\bf PicS} _ {R^{\alpha}}(R) $ the Picard monoid of the isomorphism classes of …
The commutative inverse semigroup of partial abelian extensions
This paper is a new contribution to the partial Galois theory of groups. First, given a unital
partial action αG of a finite group G on an algebra S such that S is an α G-partial Galois …
partial action αG of a finite group G on an algebra S such that S is an α G-partial Galois …
Epsilon-strongly graded rings: Azumaya algebras and partial crossed products
Let G be a group, let A=⊕ g∈ GA g be an epsilon-strongly graded ring over G, let R:= A 1 be
the homogeneous component associated with the identity of G, and let 𝙿𝚒𝚌𝚂(R) be the …
the homogeneous component associated with the identity of G, and let 𝙿𝚒𝚌𝚂(R) be the …
[HTML][HTML] Globalization of group cohomology in the sense of Alvares-Alves-Redondo
Abstract Recently ER Alvares, MM Alves and MJ Redondo introduced a cohomology for a
group G with values in a module over the partial group algebra K par (G), which is different …
group G with values in a module over the partial group algebra K par (G), which is different …
[PDF][PDF] Partial generalized crossed products (expanded version)
M Dokuchaev, I Rocha - arXiv preprint arXiv:2105.01268, 2021 - researchgate.net
Given a unital partial representation Θ of a group G into the Picard semigroup PicS (R), we
construct an abelian group C (Θ/R) formed by the isomorphism classes of generalized …
construct an abelian group C (Θ/R) formed by the isomorphism classes of generalized …
Partial generalized crossed products and a seven term exact sequence (expanded version)
M Dokuchaev, I Rocha - arXiv preprint arXiv:2105.01268, 2021 - arxiv.org
Given a non-necessarily commutative unital ring $ R $ and a unital partial representation
$\Theta $ of a group $ G $ into the Picard semigroup $\mathbf {PicS}(R) $ of the …
$\Theta $ of a group $ G $ into the Picard semigroup $\mathbf {PicS}(R) $ of the …