Related papers: Unstable modules over the Steenrod algebra revisit…
The Steenrod problem for closed orientable manifolds was solved completely by Thom. Following this approach, we solve the Steenrod problem for closed orientable orbifolds, proving that the rational homology groups of a closed orientable…
Given a special biserial algebra $\Lambda$ over an algebraically closed field, let $\mathrm{rad}_\Lambda$ denote the radical of its module category. The authors showed with Sinha that the stable rank of a special biserial algebra $\Lambda$,…
The simplices and the complexes arsing form the grading of the fundamental (desymmetrized) domain of arithmetical groups and non-arithmetical groups, as well as their extended (symmetrized) ones are described also for oriented manifolds in…
A non-unital algebra in a closed monoidal category is called self-induced if the multiplication induces an isomorphism between A\otimes_A A and A. For such an algebra, we define smoothening and roughening functors that retract the category…
Torsion pairs in the category of finitely presented modules over a noetherian ring can be parametrised by the class of cosilting modules. In this paper, we characterise such modules in terms of their indecomposable summands, providing a new…
In this paper, we construct a family of non-weight modules over the untwisted $N=2$ superconformal algebras. Those modules when regarded as modules over the Cartan subalgebra (modulo the center) are free of rank $2$. We give a…
We give some details of a simpler definition of mixed Hodge modules which has been announced in some papers. Compared with earlier arguments, this new definition is simplified by using Beilinson's maximal extension together with stability…
Suppose $\Lambda$ is a special biserial algebra over an algebraically closed field. Schr\"oer showed that if $\Lambda$ is domestic then the radical of the category of finitely generated (left) $\Lambda$-modules is nilpotent, and the least…
Support $\tau$-tilting modules correspond to some classes of categorical objects bijectively, such as two-term tilting complexes for any finite dimensional symmetric algebra. This fact motivates us to classify support $\tau$-tilting modules…
Covariant Hom-bimodules are introduced and the structure theory of them in the Hom-setting is studied in a detailed way. The category of bicovariant Hom-bimodules is proved to be a (pre)braided monoidal category and its structure theory is…
We construct a weak categorification of the quantum toroidal algebra action on the Grothendieck group of moduli space of stable (or framed) sheaves over an algebraic surface, which is constructed by Schiffmann-Vasserot and Negu\c{t}. The…
Let S(n) be the category of invariant subspaces of nilpotent operators with nilpotency index at most n. Such submodule categories have been studied already in 1936 by Birkhoff, they have attracted a lot of attention in recent years, for…
We deal with classes of prime ideals whose associated graded ring is isomorphic to the Rees algebra of the conormal module in order to describe the divisor class group of the Rees algebra and to examine the normality of the conormal module.
Any finite-dimensional Hopf algebra H is Frobenius and the stable category of H-modules is triangulated monoidal. To H-comodule algebras we assign triangulated module-categories over the stable category of H-modules. These module-categories…
We give refined bounds for the regularity of FI-modules and the stable ranges of FI-modules for various forms of their stabilization studied in the representation stability literature. We show that our bounds are sharp in several cases. We…
Let $p$ be an odd prime number. We study the problem of determining the module structure over the mod $p$ Steenrod algebra $\mathcal A(p)$ of the Dickson algebra $D_n$ consisting of all modular invariants of general linear group…
After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…
We examine the cyclic homology of the monoidal category of modules over a finite dimensional Hopf algebra, motivated by the need to demonstrate that there is a difference between the recently introduced mixed anti-Yetter-Drinfeld…
In this paper, a classification of modules of the intermediate series over the twisted N=2 superconformal algebra is obtained.
We introduce a notion of Krein C*-module over a C*-algebra and more generally over a Krein C*-algebra. Some properties of Krein C*-modules and their categories are investigated.