7 papers
Globalization of Partial Group Actions on Not Necessarily Associative Algebras and Covariant Representations
Mikhailo Dokuchaev, Emmanuel Jerez, José L. Vilca-Rodríguez
We extend the concept of a partial group action to non-associative algebras in a variety \(\mathcal{V}(I)\), solve the globalization problem within \(\mathcal{V}(I)\) and examine i…
Homology of Epsilon-Strongly Graded Algebras
Emmanuel Jerez
Let be a group and a unital epsilon-strongly -graded algebra. We construct spectral sequences converging to the Hochschild (co)homology of . Each spectral sequence is…
Twisted partial group algebra and related topological partial dynamical system
Mikhailo Dokuchaev, Emmanuel Jerez
Given a group \( G \), a field \( κ\), and a factor set \( σ\) arising from a partial projective \( κ\)-representation of \( G \). This leads to the construction of a topological p…
On the homology of partial group representations
Emmanuel Jerez
We study how the partial group (co)homology of a group with coefficient in a partial representation can be described using the usual group (co)homology. To address this, we…
The twisted partial group algebra and (co)homology of partial crossed products
Mikhailo Dokuchaev, Emmanuel Jerez
Given a group and a partial factor set of we introduce the twisted partial group algebra which governs the partial projective -representations of …
(Co)Homology of Partial Smash Products
Mikhailo Dokuchaev, Emmanuel Jerez
Given a cocommutative Hopf algebra over a commutative ring and a symmetric partial action of on a -algebra we obtain a first quadrant Grothe…
The category of partial group actions: quotients, (co)limits and groupoids
Emmanuel Jerez
We consider the category of partial actions, where the group and the set upon which the group acts can vary. Within this framework, we develop a theory of quotient partial actions…