Related papers: Finitely generated modules over quasi-Euclidean ri…

The general linear group GL(n) acts on the direct sum of $m$ copies of Mat(n) by the adjoint action. The action of GL(n) induces the action of the unitriangular subgroup U. We present the system of free generators of the field of…

Let $R$ be an algebra over a ring $\Bbbk$, $T$ an $R$-algebra, $M$ a finitely generated projective $R$-module, and $N$ a $T$-module. Let $G$ be a linearly reductive group scheme over $\Bbbk$ equipped with a representation…

Let $\Uq$ be a quantum group. Regarding a (noncommutative) space with $\Uq$-symmetry as a $\Uq$-module algebra $A$, we may think of equivariant vector bundles on $A$ as projective $A$-modules with compatible $\Uq$-action. We construct an…

Let R be a commutative Noetherian domain, and let M and N be finitely generated R-modules. We give new criteria for determining when M tensor N has torsion. We also give constructive formulas for producing a module in the isomorphism class…

A commutative ring R has finite rank r, if each ideal of R is generated at most by r elements. A commutative ring R has the r-generator property, if each finitely generated ideal of R can be generated by r elements. Such rings are closely…

We investigate properties of group gradings on matrix rings $M_n(R)$, where $R$ is an associative unital ring and $n$ is a positive integer. More precisely, we introduce very good gradings and show that any very good grading on $M_n(R)$ is…

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated quantum many-particle systems. For the simplest spinless fermion (or boson) systems with say $m$ fermions (or bosons) in $N$ single…

We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of GL_n(C) on the variety of x-nilpotent complex matrices. We obtain a criterion as to whether the action admits a finite number of orbits and specify a…

We study conditions under which subdirect products of various types of algebraic structures are finitely generated or finitely presented. In the case of two factors, we prove general results for arbitrary congruence permutable varieties,…

Let R be a ring, M a left R-module, I an infinite set, N either the direct sum or product of |I| copies of M, and E the endomorphism ring of N as a left R-module. In this note it is shown that E is not the union of a chain of |I| or fewer…

We construct a special principal series representation for the modular double $U_{q\tilde{q}}(g_R)$ of type $A_r$ representing the generators by positive essentially self-adjoint operators satisfying the transcendental relations that also…

For any countable discrete group $G$ with a reduced abelian subgroup of finite index, we construct an action $\alpha$ of $G$ on the universal UHF algebra $\Qq$ using an infinite tensor product of permutation representations of $G$ and show…

Let $R$ be a smooth affine domain of dimension $d\geq 2$ over an infinite perfect field $k$. We establish a morphism from the Euler class group $E^d(R)$ to $Um_{d+1}(R)/E_{d+1}(R)$, the group of elementary orbits of unimodular rows.

This article is devoted to the investigation of semidirect products of groups of loops and groups of diffeomorphisms of finite and infinte dimensional real, complex and quaternion manifolds. Necessary statements about quaternion manifolds…

In this work, we complete the classification of generically multiply transitive actions of groups on solvable groups in the finite Morley rank setting. We prove that if $G$ is a connected group of finite Morley rank acting definably,…

Let $G$ be an abelian group of order $n$ and let $R$ be a commutative ring which admits a homomorphism ${\Bbb Z}[\zeta_{n}]\ra R$, where $\zeta_{n}$ is a (complex) primitive $n$-th root of unity. Given a finite $R[G\e]$-module $M$, we…

Recently is has been proved that if $\sigma\in GL_n(R)$ where $R$ is an commutative ring and $n\geq 3$, then each of the elementary transvections $t_{kl}(\sigma_{ij})~(i\neq j,k\neq l)$ is a product of eight $E_n(R)$-conjugates of $\sigma$…

We study \emph{unimodular fake} $\mu's$, i.e. multiplicative functions $\mathfrak f: \N \to \mathbb{S}^1 \cup \{0\} $ determined by a fixed sequence $\{\varepsilon_k\}_{k\ge 0} \subset \mathbb{S}^1 \, \cup \, \{0\}$ via the rule $\mathfrak…

In our previous joint papers with Roozbeh Hazrat and Alexei Stepanov we established commutator formulas for relative elementary subgroups in $GL(n,R)$, $n\ge 3$, and other similar groups, such as Bak's unitary groups, or Chevalley groups.…

Larsen has recently extended Exel's construction of crossed products from single endomorphisms to abelian semigroups of endomorphisms, and here we study two families of her crossed products. First, we look at the natural action of the…