Related papers: Approximation presentations of modules and homolog…
We prove that a certain eventually homological isomorphism between module categories induces a triangle equivalence between their singularity categories, Gorenstein defect categories and the stable categories of Gorenstein projective…
In this paper, we show that the class of representable residuated semigroups has the finite representation property. That is, every finite representable residuated semigroup is representable over a finite base. This result gives a positive…
We introduce notions of finite presentation and co-exactness which serve as qualitative and quantitative analogues of finite-dimensionality for operator modules over completely contractive Banach algebras. With these notions we begin the…
This paper explores various homological regularity phenomena (in the sense of Auslander) in category $\mathcal{O}$ and its several variations and generalizations. Additionally, we address the problem of determining projective dimension of…
Results on approximate deduction in the context of the calculus of evidence of Dempster-Shafer and the theory of interval probabilities are reported. Approximate conditional knowledge about the truth of conditional propositions was assumed…
We introduce and develop an analogous of the Auslander-Buchweitz approximation theory (see \cite{AB}) in the context of triangulated categories, by using a version of relative homology in this setting. We also prove several results…
Finite versions of W-algebras are introduced by considering (symplectic) reductions of finite dimensional simple Lie algebras. In particular a finite analogue of $W^{(2)}_3$ is introduced and studied in detail. Its unitary and non-unitary,…
Let $W$ be an irreducible real reflection group. Armstrong, Reiner, and the author presented a model for parking functions attached to W and made three increasingly strong conjectures about these objects. The author generalized these…
Auslander-Reiten duality for module categories is generalised to Grothendieck abelian categories that have a sufficient supply of finitely presented objects. It is shown that Auslander-Reiten duality amounts to the fact that the functor…
The study of Property (B) starts as a special case of Lehmer's conjecture. An algebraic field is said to satisfy Property (B) if there exists a positive constant bounding by below the height of every point of infinite order. In this paper…
An extension $B\subset A$ of finite dimensional algebras is bounded if the $B$-$B$-bimodule $A/B$ is $B$-tensor nilpotent, its projective dimension is finite and $\mathrm{Tor}_i^B(A/B, (A/B)^{\otimes_B j})=0$ for all $i, j\geq 1$. We show…
We begin the study of simple finite-dimensional prime representations of quantum affine algebras from a homological perspective. Namely, we explore the relation between self extensions of simple representations and the property of being…
This article is divided into two parts. In the first part we work over a field $\mathbb{k}$ and prove that the Frobenius space associated to a Frobenius algebra is generated as left A-module by the Frobenius coproduct. In particular, we…
We consider a class of extensions of associative algebras, which we refer to as ``strongly proj-bounded extensions''. We prove that the finiteness of the left global dimension and the support of the Hochschild homology is preserved by…
In this presentation, I review physical principles behind a recently proposed \cite{smw-utr} Universal Theory of Relativity and speculate on the mathematical requirements implied by these physical principles. Some unresolved issues will…
We classify the finite dimensional irreducible representations of rectangular finite $W$-algebras, i.e., the finite $W$-algebras $U(\mathfrak{g}, e)$ where $\mathfrak{g}$ is a symplectic or orthogonal Lie algebra and $e \in \mathfrak{g}$ is…
We study property A for metric spaces $X$ with bounded geometry introduced by Guoliang Yu. Property A is an amenability-type condition, which is less restrictive than amenability for groups. The property has a connection with…
We investigate the structure of certain almost split sequences in $\mathcal{P}(\Lambda)$, i.e., the category of morphisms between projective modules over an Artin algebra $\Lambda$. The category $\mathcal{P}(\Lambda)$ has very nice…
We consider a set $\mbK = \bigcup_{n \in \mbbN}\mbK_n$ of {\em finite} structures such that all members of $\mbK_n$ have the same universe, the cardinality of which approaches $\infty$ as $n\to\infty$. Each structure in $\mbK$ may have a…
Given a faithful finite-dimensional representation $V$ of a finite group $G$ over any field $\mathbb{F}$, we show that any irreducible ${\mathbb{F}}G$-module $W$ appears, as a submodule or a quotient, in $\mathrm{Sym}^m(V)$ for some integer…