arXiv subjects

Dirceu Bagio

Publications and source records attributed to Dirceu Bagio.

24 records · Page 2Linked to original sources

arXiv2018

Lifting partial actions: from groups to groupoids

In this paper, we are interested in the study of the existence of connections between partial groupoid actions and partial group actions. Precisely, we prove that there exists a datum connecting a partial action of a connected groupoid and a partial action of any of its isotropy groups. Furthermore, it will be proved that under a suitable condition the partial skew groupoid ring corresponding to a partial action by a connected groupoid is isomorphic to a specific partial skew group ring. We also present a Morita theory and a Galois theory related to these partial actions as well as considerations about the strictness of the corresponding Morita contexts. Semisimplicity, separability and Frobenius properties of the corresponding partial skew groupoid rings are also considered.

math.RA↗

arXiv2017

On the separability of the partial skew groupoid ring

Given a partial (resp. a global) action $α$ of a connected finite groupoid $G$ on a ring $A$, we determine necessary and sufficient conditions for the partial (resp. global) skew groupoid ring $A\star_α G$ to be a separable extension of $A$.

math.RA↗

arXiv2017

Representations of the super Jordan plane

It is shown that the finite-dimensional simple representations of the super Jordan plane $B$ are one-dimensional. The indecomposable representations of dimension $2$ and $3$ of $B$ are classified. Two families of indecomposable representations of $B$ of arbitrary dimension are presented.

math.QA↗

arXiv2015

Inner Actions of Weak Hopf Algebras

Let $R$ be an associative ring and $e,f$ idempotent elements of $R$. In this paper we introduce the notion of $(e,f)$-invertibility for an element of $R$ and use it to define inner actions of weak Hopf algebras. Given a weak Hopf algebra $H$ and an algebra $A$, we present sufficient conditions for $A$ to admit an inner action of $H$. We also prove that if $A$ is a left $H$-module algebra then $H$ acts innerly on the smash product $A\#H$ if and only if $H$ is a quantum commutative weak Hopf algebra.

math.QA↗

arXiv2012

Examples of pointed color Hopf algebras

We present examples of color Hopf algebras, i.e. Hopf algebras in color categories (braided tensor categories with braiding induced by a bicharacter on an abelian group), related with quantum doubles of pointed Hopf algebras. We also discuss semisimple color Hopf algebras.

math.QA↗

arXiv2011

Partial groupoid actions: globalization, Morita theory and Galois theory

In this paper we introduce the notion of a partial action of a groupoid on a ring as well as we give a criteria for the existence of a globalization of it. We construct a Morita context associated to a globalizable partial groupoid action and we introduce the notion of a partial Galois extension, which is related to the strictness of this context.

math.RA↗