Related papers: Modules of Abelian integrals and Picard-Fuchs syst…

Motivated by the study of von Neumann regular skew groups as carried out by Alfaro, Ara and del Rio in 1995 we investigate regular and biregular Hopf module algebras. If $A$ is an algebra with an action by an affine Hopf algebra $H$, then…

We present a study of the homological algebra of bimodules over $A_\infty$-algebras endowed with an involution. Furthermore we introduce a derived description of Hochschild homology and cohomology for involutive $A_\infty$-algebras.

For a fixed finite group $Q$ and semi-simple finite dimensional algebra $S$, we examine an equivalence between strongly $Q$-graded algebras (extensions) with identity component $S$ and $S^1$-gerbes on action groupoids of $Q$ on the set of…

We exhibit how the Hodge-Deligne moduli space of $\lambda$-connections over a smooth projective curve, for stable bundles with fixed determinant, can be understood as the dual of the Atiyah algebroid of the determinant of cohomology line…

We generalise a result of Fourquaux and Xie thereby completely determining the relationship between $\mathbb{Q}_p$ and $L$-analytic Lie algebra cohomology of analytic $(\varphi_L,\Gamma_L)$-modules. We use the results to conclude that for…

The theory of multiplier modules of Hilbert C*-modules is reconsidered to obtain more properties of these special Hilbert C*-modules. The property of a Hilbert C*-module to be a multiplier C*-module is shown to be an invariant with respect…

In this paper, we give an explicit chain map, which induces the algebra isomorphism between the Hochschild cohomology ${\bf HH}^{\bullet}(B)$ and the $H$-invariant subalgebra ${\bf H}^{\bullet}(A, B)^{H}$ under two mild hypotheses, where…

We define cohomology of associative H-pseudoalgebras, and we show that it describes module extensions, abelian pseudoalgebra extensions, and pseudoalgebra first order deformations. We describe in details the same results for the special…

For any finite-dimensional factorizable ribbon Hopf algebra H and any ribbon automorphism omega of H, we establish the existence of the following structure: an H-bimodule F_omega and a bimodule morphism Z_omega from Lyubashenko's Hopf…

Let $d$ be a positive integer. In a previous article we established a bijective correspondence between the following classes of objects, considered up to the appropriate notion of equivalence: differential graded algebras with…

This is the addendum to the paper "On the Multiplicity Problem and the Isomorphism Problem for the Four Subspace Algebra" Communications in Algebra, 40:6 (2012), 2005-2036 (DOI: 10.1080/00927872.2011.570830). We give here the full proof of…

We study the vanishing of (co)homology along ring homomorphisms for modules that admit certain filtrations, and generalize a theorem of O. Celikbas-Takahashi. Our work produces new classes of rigid and test modules, in particular over local…

The authors define an "anti-holomorphic" involution (or "real structure") on an ordinary Abelian variety (defined over a finite field k) to be an involution of the associated Deligne module (T,F,V) that exchanges F (the Frobenius) with V…

Let $A$ be a $C^*$-algebra, $H$ be a Hilbert $A$-module and $K(H)$ be the closure of the set of finite rank module maps. We show that the $W^*$-algebra of all bounded $A^{**}$-module maps on the smallest self-dual Hilbert $A^{**}$-module…

The aim of the present paper is to describe self-duality and C*- reflexivity of Hilbert {\bf A}-modules $\cal M$ over monotone complete C*-algebras {\bf A} by the completeness of the unit ball of $\cal M$ with respect to two types of…

Let $A$ and $B$ be arbitrary $C^*$-algebras, we prove that the existence of a Hilbert $A$-$B$-bimodule of finite index ensures that the WEP, QWEP, and LLP along with other finite-dimensional approximation properties such as CBAP and (S)OAP…

We prove that the cohomology class of any curve on a very general principally polarized abelian variety of dimension at least 4 is an even multiple of the minimal class. The same holds for the intermediate Jacobian of a very general cubic…

In this note we classify some integrable invariant Sobolev metrics on the Abelian extension of the diffeomorphism group of the circle. We also derive a new two-component generalization of the Camassa-Holm equation. The system obtained…

We use the adelic language to show that any homomorphism between Jacobians of modular curves arises from a linear combination of Hecke modular correspondences. The proof is based on a study of the actions of $\mathrm{GL}_2$ and Galois on…

We investigate relative cohomology functors on subcategories of abelian categories via Auslander-Buchweitz approximations and the resulting strict resolutions. We verify that certain comparison maps between these functors are isomorphisms…