Related papers: On invertibility preserving linear maps, simultane…

Let $K$ be an arbitrary field of characteristic zero and $A$ a commutative associative $ K$-algebra which is an integral domain. Denote by $R$ the fraction field of $A$ and by $W(A)=RDer_{\mathbb K}A,$ the Lie algebra of $\mathbb…

Let $K$ be a field of characteristic different from 2 and let $G$ be a group. If the algebra $UT_n$ of $n\times n$ upper triangular matrices over $K$ is endowed with a $G$-grading $\Gamma: UT_n=\oplus_{g\in G}A_g$ we give necessary and…

Let k be an algebraically closed field of characteristic zero, F its algebraically closed extension, and G be the group of k-automorphisms of F endowed with a natural topology. One of the purposes of this paper is to show that any…

This article is the first of two where we investigate to what extent homotopy invariant, excisive and matrix stable homology theories help one distinguish between the Leavitt path algebras $L(E)$ and $L(F)$ of graphs $E$ and $F$ over a…

We find a necessary and sufficient condition for the existence of the tensor product of modules over a Lie conformal algebra. We provide two algebraic constructions of the tensor product. We show the relation between tensor product and…

We study new classes of linear preservers between C$^*$-algebras and JB$^*$-triples. Let $E$ and $F$ be JB$^*$-triples with $\partial_{e} (E_1)$. We prove that every linear map $T:E\to F$ strongly preserving Brown-Pedersen quasi-invertible…

An $n \times n$ matrix $H$ is Butson-Hadamard if its entries are $k^{\text{th}}$ roots of unity and it satisfies $HH^* = nI_n$. Write $BH(n, k)$ for the set of such matrices. Suppose that $k = p^{\alpha}q^{\beta}$ where $p$ and $q$ are…

Let $A$ be a separable, unital and exact $C^*$-algebra satisfying the universal coefficient theorem. We prove uniqueness theorems up to unitary conjugacy for unital, full and nuclear maps from $A$ into ultraproducts of finite von Neumann…

This paper concerns the enumeration of isomorphism classes of modules of a polynomial algebra in several variables over a finite field. This is the same as the classification of commuting tuples of matrices over a finite field up to…

For $k\in\mathbb R$, we consider a $\mathbb C$-algebra $\mathcal A_k$ of holomorphic functions in the half plane $Re\; z>k$ with (at most) subexponential growth on the real line to $+\infty$. In the $\mathcal A_k$-algebra of sequences of…

We consider typical finite dimensional complex irreducible representations of a basic classical simple Lie superalgebra, and give a sufficient condition on when unique factorization of finite tensor products of such representations hold. We…

Given a set of forms f={f_1,...,f_m} in R=k[x_1,...,x_n], where k is a field of characteristic zero, we focus on the first syzygy module Z of the transposed Jacobian module D(f), whose elements are called differential syzygies of f. There…

We prove that it is consistent with ZFC that every unital endomorphism of the Calkin algebra $\mathcal{Q}(H)$ is unitarily equivalent to an endomorphism of $\mathcal{Q}(H)$ which is liftable to a unital endomorphism of $\mathcal{B}(H)$. We…

Given a finite dimensional algebra $A$ over an algebraically closed field we study the relationship between the powers of the radical of a morphism in the module category of the algebra $A$ and the induced morphism in the module category of…

For a homomorphism f: A --> B of commutative rings, let D(A,B) denote Ker[Pic(A) --> Pic(B)]. Let k be a field and assume that A is a f.g. k-algebra. We prove a number of finiteness results for D(A,B). Here are four of them. 1: Suppose B is…

Our aim in this paper is to study the global invertibility of a locally Lipschitz map $f:X \to Y$ between (possibly infinite-dimensional) Finsler manifolds, stressing the connections with covering properties and metric regularity of $f$. To…

We prove that a linear mapping on the algebra \(\mathfrak{sl}_n\) of all trace zero complex matrices is a local automorphism if and only if it is an automorphism or an anti-automorphism. We also show that a linear mapping on a simple…

A general position map $f:K\to M$ of a $k$-dimensional simplicial complex to a $2k$-dimensional manifold (for $k=1$, of a graph to a surface) is a $\mathbb Z_2$-embedding if $|f\sigma \cap f\tau|$ is even for any non-adjacent $k$-faces…

Let $n,k$ be fixed natural numbers with $1\le k\le n$ and let $A_{n+1,k,2k,\dots,sk}$ denote an $(n+1)\times (n+1)$ complex multidiagonal matrix having $s=[n/k]$ sub- and superdiagonals at distances $k,2k,\dots,sk$ from the main diagonal.…

In a recent paper, a new method was proposed to find the common invariant subspaces of a set of matrices. This paper invstigates the more general problem of putting a set of matrices into block triangular or block-diagonal form…