Related papers: On module categories over finite-dimensional Hopf …

For a left coherent ring A with every left ideal having a countable set of generators, we show that the coderived category of left A-modules is compactly generated by the bounded derived category of finitely presented left A-modules…

Given a Hopf algebra A, there exist various cohomology theories for the category of Hopf bimodules over A, introduced by M. Gerstenhaber and S.D. Schack, and by C. Ospel. We prove, when A is finite dimensional, that they are equal to the…

In this paper, we study pointed rank one Hopf algebras and Hopf-Ore extensions of group algebras, over an arbitrary field $k$. It is proved that the rank of a Hopf-Ore extension of a group algebra is one or two or infinite. It is also shown…

We introduce the notions of categorical integrals and categorical cointegrals of a finite tensor category $\mathcal{C}$ by using a certain adjunction between $\mathcal{C}$ and its Drinfeld center $\mathcal{Z}(\mathcal{C})$. These notions…

We give a solution, via operator spaces, of an old problem in the Morita equivalence of C*-algebras. Namely, we show that C*-algebras are strongly Morita equivalent in the sense of Rieffel if and only if their categories of left operator…

We define a version of Hochschild homology and cohomology suitable for a class of algebras admitting compatible actions of bialgebras, called module algebras. We show this (co)homology, called Hopf--Hochschild (co)homology, can also be…

We study the combinatorics of the category F of finite-dimensional modules for the orthosymplectic Lie supergroup OSP(r|2n). In particular we present a positive counting formula for the dimension of the space of homomorphism between two…

Let $\mathcal{C}$ be a finite braided multitensor category. Let $B$ be Majid's automorphism braided group of $\mathcal{C}$, then $B$ is a cocommutative Hopf algebra in $\mathcal{C}$. We show that the center of $\mathcal{C}$ is isomorphic to…

Comodule algebras of a Hopf algebroid H with a bijective antipode, i.e. algebra extensions B\subseteq A by H, are studied. Assuming that a lifted canonical map is a split epimorphism of modules of the non-commutative base algebra of H,…

In this paper we classify irreducible integrable representations of loop toroidal Lie algebras with finite dimensional weight spaces. In both the cases we classify modules, when a part of center acts non-trivially and trivially on modules.

In this note the categories of coefficients for Hopf cyclic cohomology of comodule algebras and comodule coalgebras are extended. We show that these new categories have two proper different subcategories where the smallest one is the known…

For a semisimple quasi-triangular Hopf algebra $\left( H,R\right) $ over a field $k$ of characteristic zero, and a strongly separable quantum commutative $H$-module algebra $A$ over which the Drinfeld element of $H$ acts trivially, we show…

We transpose Jones' technology and the authors' C*-algebraic techniques to study representations of the Leavitt path algebra L (over an arbitrary row-finite graph) by using its quiver algebra A. We establish an equivalence of categories…

The classification of finite-dimensional pointed Hopf algebras with group S_3 was finished in "The Nichols algebra of a semisimple Yetter-Drinfeld module", arXiv:0803.2430v1 [math.QA], by Andruskiewitsch, Heckenberger and Schneider: there…

Let $C$ be a symmetrizable generalized Cartan matrix with symmetrizer $D$ and orientation $\Omega$. In previous work we associated an algebra $H$ to this data, such that the locally free $H$-modules behave in many aspects like…

Let H be a finite-dimensional Hopf algebra. We give a description of the tensor product of bimodule categories over Rep(H). When the bimodule categories are invertible this description can be given explicitly. We present some consequences…

Motivated by the relation between Schur algebra and the group algebra of a symmetric group, along with other similar examples in algebraic Lie theory, Min Fang and Steffen Koenig addressed some behaviour of the endomorphism algebra of a…

The aim of this paper is an algebraic study of the Hopf algebra H_R of rooted trees, which was introduced in \cite{Kreimer1,Connes,Broadhurst,Kreimer2}. We first construct comodules over H_R from finite families of primitive elements.…

We study the basic monoidal properties of the category of Hopf modules for a coquasi Hopf algebra. In particular we discuss the so called fundamental theorem that establishes a monoidal equivalence between the category of comodules and the…

We obtain a complete classification of all finite-dimensional irreducible modules over classical map superalgebras, provide formulas for their (super)characters and a description of their extension groups. Furthermore, we describe the block…