Costoya, Cristina Méndez, David Viruel, Antonio
Published in
Mediterranean Journal of Mathematics

Let H be an arbitrary group and let ρ:H→Sym(V)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho :H\rightarrow {\text {Sym}}(V)$$\end{document} be any permutation rep...

Positselski, Leonid
Published in
Algebras and Representation Theory

We present the definition of a dedualizing complex of bicomodules over a pair of cocoherent coassociative coalgebras C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\ma...

Zhang, Xiaohui Guo, Shuangjian Wang, Shengxiang
Published in
Advances in Applied Clifford Algebras

The main purpose of the present paper is to develop the theory of center constructions on Hom–Hopf algebras. Let H be a Hom–Hopf algebra, we first introduce the notions of nth Yetter–Drinfeld modules and mth Drinfeld codouble for H. Also we prove that the category YDHH(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepa...

Sore, W. Hermann B.
Published in
Journal of Homotopy and Related Structures

We prove that the normalization functor of the Dold-Kan correspondence does not induce a Quillen equivalence between Goerss’ model category of simplicial coalgebras and Getzler–Goerss’ model category of differential graded coalgebras.

Dokuchaev, M.
Published in
São Paulo Journal of Mathematical Sciences

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 actions of semigroups, of Hopf algebras and groupoids, the globalization problem for partial actions, Morita theory of partial actions, twisted partial actions, partial proj...

Chirvasitu, Alexandru Penkov, Ivan
Published in
Algebras and Representation Theory

We introduce (partially) ordered Grothendieck categories and apply results on their structure to the study of categories of representations of the Mackey Lie algebra of infinite matrices 𝔤𝔩MV,V∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...

Crivei, Septimiu Olteanu, Gabriela
Published in
Applied Categorical Structures

We study the transfer of (dual) relative Rickart properties via functors between abelian categories, and we deduce the transfer of (dual) relative Baer property. We also give applications to Grothendieck categories, comodule categories and (graded) module categories, with emphasis on endomorphism rings.

Aguiar, Marcelo Haim, Mariana López Franco, Ignacio
Published in
Applied Categorical Structures

We study the action of monads on categories equipped with several monoidal structures. We identify the structure and conditions that guarantee that the higher monoidal structure is inherited by the category of algebras over the monad. Monoidal monads and comonoidal monads appear as the base cases in this hierarchy. Monads acting on duoidal categori...

Mohamed, Mohamed Belhaj Manchon, Dominique
Published in
Letters in Mathematical Physics

The vector space spanned by rooted forests admits two graded bialgebra structures. The first is defined by Connes and Kreimer using admissible cuts, and the second is defined by Calaque, Ebrahimi-Fard and the second author using contraction of trees. In this article, we define the doubling of these two spaces. We construct two bialgebra structures ...

Fan, Zhong-ping Lu, Di-ming Yu, Xiao-lan
Published in
Applied Mathematics-A Journal of Chinese Universities

In this paper, we study non-cosemisimple Hopf algebras through their underlying coalgebra structure. We introduce the concept of the maximal pointed subcoalgebra/Hopf subalgebra. For a non-cosemisimple Hopf algebra A with the Chevalley property, if its diagram is a Nichols algebra, then the diagram of its maximal pointed Hopf subalgebra is also a N...