Related papers: $\omega$-left approximation dimensions under Stabl…
The article is devoted to the investigation of properties of quasi-invariant measures with values in non-Archimedean fields such as: convolutions of measures and functions; continuity of functions of measures; non-associative noncommutative…
In this paper, we present a method to construct new stable equivalences of Morita type. Suppose that a stable equivalence of Morita type between finite dimensional algebras $A$ and $B$ is defined by a $B$-$A$-bimodule $N$. Then, for any…
We give a new proof, by using simplified terminology and notation, to a result of Puig stating that if a bimodule of two block algebras of finite groups over an algebraically closed field induces a stable equivalence of Morita type and has…
We uncover a connection between the model-theoretic notion of superstability and that of noetherian rings and pure-semisimple rings. We characterize noetherian rings via superstability of the class of left modules with embeddings.…
Let $R$ be a ring and $T$ be a good Wakamatsu-tilting module with $S$ the endomorphism ring. We prove that $T$ induces an equivalence between stable categories of repetitive algebras of $R$ and $S$.
We deduce the Kazhdan-Lusztig conjecture on the multiplicities of simple modules over a simple complex Lie algebra in Verma modules in category O from the equivariant geometric Satake correspondence and the analysis of torus fixed points in…
The algebraic stability theorem for $\mathbb{R}$-persistence modules is a fundamental result in topological data analysis. We present a stability theorem for $n$-dimensional rectangle decomposable persistence modules up to a constant…
A duality theorem of the bounded derived category of quasi-finite comodules over an artinian coalgebra is established. Let $A$ be a noetherian complete basic semiperfect algebra over an algebraically closed field, and $C$ be its dual…
The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups…
Our main result (Theorem 1) suggests a possible dividing line ($\mu$-superstable $+$ $\mu$-symmetric) for abstract elementary classes without using extra set-theoretic assumptions or tameness. This theorem illuminates the structural side of…
We study the relation (and differences) between stability and Property (S) in the simple and stably finite framework. This leads us to characterize stable elements in terms of its support, and study these concepts from different sides :…
In representation theory of graded Iwanaga-Gorenstein algebras, tilting theory of the stable category $\underline{\mathsf{CM}}^{\mathbb{Z}} A$ of graded Cohen-Macaulay modules plays a prominent role. In this paper we study the following two…
In this paper, we study the stability and convergence of some general quadratic semimartingales. Motivated by financial applications, we study simultaneously the semimartingale and its opposite. Their characterization and integrability…
Tilting theory is one of the central tools in modern representation theory, in particular in the study of Cohen-Macaulay representations. We study Cohen-Macaulay representations of $\mathbb N$-graded Artin-Schelter Gorenstein algebras $A$…
Let $X$ be a compact complex manifold of dimension $n$ and let $m$ be a positive integer with $m\leq n$. Assume that $X$ admits a K\"ahler metric $\omega$ and a weakly positive, $\partial\bar\partial$-closed, smooth $(n-m,\,n-m)$-form…
On a polarised surface, solutions of the Vafa-Witten equations correspond to certain polystable Higgs pairs. When stability and semistability coincide, the moduli space admits a symmetric obstruction theory and a $\mathbb C^*$ action with…
We study the Artin Approximation property with constraints in a different frame. As a consequence we give a nested Artin Strong Approximation property for algebraic power series rings over a field.
We first propose a generalization of the notion of Mathieu subspaces of associative algebras $\mathcal A$, which was introduced recently in [Z4] and [Z6], to $\mathcal A$-modules $\mathcal M$. The newly introduced notion in a certain sense…
We study the positivity of CM line bundles on the coarse moduli space of Kawamata log terminal (klt) good minimal models with Kodaira dimension one. We prove that the seminormalization of the moduli space is quasi-projective under a mild…
We prove some structure results for isometries between noncommutative Lp spaces associated to von Neumann algebras. We find that an isometry T: Lp(M_1) to Lp(M_2) (1 le p < infty, p not 2) can be canonically expressed in a certain simple…