Related papers: Derived and stable equivalences of centralizer mat…
Based on the fact that every finite-dimensional algebra over a field is isomorphic to the centralizer of \textbf{two} matrices, we approach the representation theory of finite-dimensional algebras over fields by centralizers of matrices.…
As is known, every finite-dimensional algebra over a field is isomorphic to the centralizer algebra of \textbf{two} matrices. So it is fundamental to study first the centralizer algebra of a single matrix, called a centralizer matrix…
The centralizer algebra of a matrix consists of those matrices that commute with it. We investigate the basic representation-theoretic invariants of centralizer algebras, namely their radicals, projective indecomposable modules, injective…
The fact that each finite-dimensional algebra over a field is isomorphic to the centralizer of two matrices, has suggested to investigate representation theoretical problems of finite-dimensional algebras through centralizer algebras of…
In this brief postscript to our paper "Integral transforms and Drinfeld centers in derived algebraic geometry", we describe a Morita equivalence for derived, categorified matrix algebras implied by theory developed since its appearance. We…
We describe Morita equivalence of unital locally matrix algebras in terms of their Steinitz parametrization. Two countable dimensional unital locally matrix algebras are Morita equivalent if and only if their Steinitz numbers are rationally…
It is known that that the centralizer of a matrix over a finite field depends, up to conjugacy, only on the type of the matrix, in the sense defined by J. A. Green. In this paper an analogue of the type invariant is defined that in general…
For self-injective algebras, Rickard proved that each derived equivalence induces a stable equivalence of Morita type. For general algebras, it is unknown when a derived equivalence implies a stable equivalence of Morita type. In this…
Centrosymmetric matrices of order $n$ over an arbitrary algebra $R$ form a subalgebra of the full $n\times n$ matrix algebra over $R$. It is called the centrosymmetric matrix algebra of order $n$ over $R$ and denoted by $S_n(R)$. We prove…
We define an algebra $A$ to be centrally stable if, for every epimorhism $\varphi$ from $A$ to another algebra $B$, the center $Z(B)$ of $B$ is equal to $\varphi(Z(A))$, the image of the center of $A$. After providing some examples and…
We consider algebras in a modular tensor category C. If the trace pairing of an algebra A in C is non-degenerate we associate to A a commutative algebra Z(A), called the full centre, in a doubled version of the category C. We prove that two…
A description of tilting complexes is given for a class of PI algebras whose prime spectrum is canonically homeomorphic to the prime spectrum of its center. Some Sklyanin algebras are the kind of algebras considered. As an application, it…
In a recent paper \cite{HuXi3}, we introduced a classes of derived equivalences called almost $\nu$-stable derived equivalences. The most important property is that an almost $\nu$-stable derived equivalence always induces a stable…
This article is devoted to the study of the centralizer and the clifforder of a matrix over a field $\mathbb{F}$ of characteristic zero, as well as the quasi-commutative relations between matrices over the complex field $\mathbb{C}$. We…
A linear mapping $\phi$ on an algebra $\mathcal{A}$ is called a centralizable mapping at $G\in\mathcal{A}$ if $\phi(AB)=\phi(A)B=A\phi(B)$ for each $A$ and $B$ in $\mathcal{A}$ with $AB=G$, and $\phi$ is called a derivable mapping at…
Let $\mathfrak{g}$ be a finite-dimensional real or complex Lie algebra, and let $\mu \in \mathfrak{g}^{*}$. In the first part of the paper, the relation is discussed between the derived algebra of the stabilizer of $\mu$ and the set of…
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 introduce a Morita type equivalence: two operator algebras $A$ and $B$ are called strongly $\Delta $-equivalent if they have completely isometric representations $\alpha $ and $\beta $ respectively and there exists a ternary ring of…
We define a notion of equivalence between algebraic dependent type theories which we call Morita equivalence. This notion has a simple syntactic description and an equivalent description in terms of models of the theories. The category of…
Two rings A and B are said to be derived Morita equivalent if their derived categories of modules are equivalent. By results of Rickard, if A and B are derived Morita equivalent algebras over a field k, then there is a complex of bimodules…