Related papers: Yetter-Drinfeld modules for Hom-bialgebras

We study the biclosedness of the monoidal categories of modules and comodules over a (left or right) Hopf algebroid, along with the bimodule category centres of the respective opposite categories and a corresponding categorical equivalence…

We prove that the category of dg-modules and dg-algebras in a Grothendieck quasi-abelian category are endowed with a Quillen model structure. This allows some flexibility in setting up a theory of derived algebraic geometry in the infinite…

We show that the category of partial modules over a Hopf algebra $H$ is a biactegory (a bimodule category) over the category of global $H$-modules. The corresponding enrichment of partial modules over global modules is described, and the…

Our work is motivated by obtaining solutions to the quantum reflection equation (qRE) by categorical methods. To start, given a braided monoidal category $\mathcal{C}$ and $\mathcal{C}$-module category $\mathcal{M}$, we introduce a version…

Hom-bialgebras and Hom-Hopf algebras are generalizations of bialgebra and Hopf algebra structures, where associativity and coassociativity conditions are twisted by a homomorphism. The purpose of this paper is to define a…

In representation theory of finite-dimensional algebras, (semi)bricks are a generalization of (semi)simple modules, and they have long been studied. The aim of this paper is to study semibricks from the point of view of $\tau$-tilting…

Under suitable assumptions on the base field, we prove that a commutative semisimple Yetter-Drinfel'd Hopf algebra over a finite abelian group is trivial, i.e., is an ordinary Hopf algebra, if its dimension is relatively prime to the order…

Let K be a comonad on a model category M. We provide conditions under which the associated category of K-coalgebras admits a model category structure such that the forgetful functor to M creates both cofibrations and weak equivalences. We…

We define algebras of quasi-quaternion type, which are symmetric algebras of tame representation type whose stable module category has certain structure similar to that of the algebras of quaternion type introduced by Erdmann. We observe…

We prove that a finite-dimensional Hopf algebra with the dual Chevalley Property over a field of characteristic zero is quasi-isomorphic to a Radford-Majid bosonization whenever the third Hochschild cohomology group in the category of…

We present resent results regarding invertible, non-degenerate solutions of the set-theoretic Yang-Baxter and reflection equations. We recall the notion of braces and we present and prove various fundamental properties required for the…

We introduce a general framework for associating to a homogeneous quantum principal bundle a Yetter-Drinfeld module structure on the cotangent space of the base calculus. The holomorphic and anti-holomorphic Heckenberger-Kolb calculi of the…

In this paper, first we recall the notion of Hom-Jordan superalgebras and study their representations. We define the Yang-Baxter equation in a Hom-Jordan superalgebra. Additionally, we extend the connections between $\mathcal {O}$-operators…

Let $H$ be a Hopf algebra and $\mathcal{LR}(H)$ the category of Yetter-Drinfel'd-Long bimodules over $H$. We first give sufficient and necessary conditions for $\mathcal{LR}(H)$ to be symmetry and pseudosymmetry, respectively. We then…

In arXiv:1104.4441 it was shown that any 1-quasi-hereditary algebra affords a particular basis which is related to a given partial order on the set of simple modules. We show that the modules generated by these basis-elements are also…

For $d\geq 1$, we define semibricks and wide subcategories in the $d$-extended hearts of bounded $t$-structures on a triangulated category. We show that these semibricks are in bijection with finite-length wide subcategories. When the…

Dlab and Ringel showed that algebras being quasi-hereditary in all total orders for indices of primitive idempotents becomes hereditary. So, we are interested in for which orders a given quasi-hereditary algebra is again quasi-hereditary.…

A hom-associative structure is a set $A$ together with a binary operation $\star$ and a selfmap $\alpha$ such that an $\alpha$-twisted version of associativity is fulfilled. In this paper, we assume that $\alpha$ is surjective. We show that…

We construct a new model structure on the category of dg presheaves over a topological space $X$, obtained through the right Bousfield localization of the local projective model structure. The motivation for this construction arises from…

A quasi-Hopf algebra $H$ can be seen as a commutative algebra $A$ in the centre $\mathcal Z(H-Mod)$ of $H-Mod$. We show that the category of $A$-modules in $\mathcal Z(H-Mod)$ is equivalent (as a monoidal category) to $H-Mod$. This can be…