Related papers: Doi-Koppinen modules for quantum groupoids

This article develops several main results for a general theory of homological algebra in categories such as the category of sheaves of idempotent modules over a topos. In the analogy with the development of homological algebra for abelian…

Let $H$ be a finite dimensional quasi-Hopf algebra over a field $k$ and ${\mathfrak A}$ a right $H$-comodule algebra in the sense of Hausser and Nill. We first show that on the $k$-vector space ${\mathfrak A}\ot H^*$ we can define an…

We introduce procellular algebras, so called because they are inverse limits of finite dimensional cellular algebras as defined by Graham and Lehrer. A procellular algebra is defined as a certain completion of an infinite dimensional…

To any bimodule which is finitely generated and projective on one side one can associate a coring, known as a comatrix coring. A new description of comatrix corings in terms of data reminiscent of a Morita context is given. It is also…

We introduce the concept of Loday algebroids, a generalization of Courant algebroids. We define the naive cohomology and modular class of a Loday algebroid, and we show that the modular class of the double of a Lie bialgebroid vanishes. For…

The relationship between comodules of a coring and flat connections is reviewed. In particular we specialise to corings which are built on a tensor product of algebra and a coalgebra. Such corings are in one-to-one correspondence with…

We introduce a multi-parameter twisted Hopf algebra associated with a root datum and show that its modified form is isomorphic to Lusztig's modified quantum algebra under certain restrictions on the parameters. By taking various…

We introduce a notion of duality for a Lie-Rinehart algebra giving certain bilinear pairings in its cohomology generalizing the usual notions of Poincar\'e duality in Lie algebra cohomology and de Rham cohomology. We show that the duality…

In this work we introduce the notions of Peiffer product and Peiffer commutator of internal pre-crossed modules over a fixed object B, extending the corresponding classical notions to any semi-abelian category C. We prove that, under mild…

The purpose of this paper is to introduce the notion of noncommutative BiHom-pre-Poisson algebra. Also we establish the bimodules and matched pairs of noncommutative BiHom-(pre)-Poisson algebras and related relevant properties are also…

The internal bialgebroid -- in a symmetric monoidal category with coequalizers -- is defined. The axioms are formulated in terms of internal entwining structures and alternatively, in terms of internal corings. The Galois property of the…

Contramodules are module-like algebraic structures endowed with infinite summation (or, occasionally, integration) operations satisfying natural axioms. Introduced originally by Eilenberg and Moore in 1965 in the case of coalgebras over…

An orbifold datum is a collection $\mathbb{A}$ of algebraic data in a modular fusion category $\mathcal{C}$. It allows one to define a new modular fusion category $\mathcal{C}_{\mathbb{A}}$ in a construction that is a generalisation of…

Let $U_q'(\mathfrak{g})$ be a quantum affine algebra of arbitrary type and let $\mathcal{C}_{\mathfrak{g}}$ be Hernandez-Leclerc's category. We can associate the quantum affine Schur-Weyl duality functor $F_D$ to a duality datum $D$ in…

Generalising a result for Hopf algebras, we not only define the four possible types of Hopf modules in the bialgebroid setting but also yield the notion of two-sided two-cosided Hopf modules, also known as Hopf bimodules or tetramodules, in…

Let $A \subseteq E$ be an extension of Hopf algebras such that there exists a normal left $A$-module coalgebra map $\pi : E \to A$ that splits the inclusion. We shall describe the set of all coquasitriangular structures on the Hopf algebra…

To a B-coring and a (B,A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule…

In this work we study some properties of comldules over (non-cosemisimple) Hopf algebras possessing integrals, which are also called co-Frobenius Hopf algebras. We apply the result obtained to the classification of representations of…

We introduce a noncommutative and noncocommutative Hopf algebra which takes for certain Hopf categories (and therefore braided monoidal bicategories) a similar role as the Grothendieck- Teichmueller group for quasitensor categories. We also…

We introduce Hopf categories enriched over braided monoidal categories. The notion is linked to several recently developed notions in Hopf algebra theory, such as Hopf group (co)algebras, weak Hopf algebras and duoidal categories. We…