Related papers: Centralizers in non-associative rings with a pseud…

Let $G$ be a group and let $R$ be a $G$-graded ring. We show that a nonzero central idempotent in $R$ has finite support group in two broad settings: when $G$ is abelian, and when $G$ is arbitrary but the grading satisfies a certain…

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…

In this paper we show that the center of the partition algebra $\mathcal{A}_{2k}(\delta)$, in the semisimple case, is given by the subalgebra of supersymmetric polynomials in the normalised Jucys-Murphy elements. For the non-semisimple…

We extend results on transitive self-similar abelian subgroups of the group of automorphisms $\mathcal{A}_m$ of an $m$-ary tree $\mathcal{T}_m$ in \cite{BS}, to the general case where the permutation group induced on the first level of the…

Finite W-algebras are certain associative algebras arising in Lie theory. Each W-algebra is constructed from a pair of a semisimple Lie algebra g (our base field is algebraically closed and of characteristic 0) and its nilpotent element e.…

In this paper, we study the action of finite subgroups of the mapping class group of a surface on the curve complex. We prove that if the diameter of the almost fixed point set of a finite subgroup H is big enough, then the centralizer of H…

A centrally essential ring is a ring which is an essential extension of its center (we consider the ring as a module over its center). We give several examples of noncommutative centrally essential rings and describe some properties of…

For a finite dimensional complex Lie algebra, its index is the minimal dimension of stabilizers for the coadjoint action. A famous conjecture due to Elashvili says that the index of the centralizer of an element of a reductive Lie algebra…

An associative central simple algebra is a form of matrices, because a maximal \'{e}tale subalgebra acts on the algebra faithfully by left and right multiplication. In an attempt to extract and isolate the full potential of this point of…

Let $\hat\Z_p$ be the ring of $p$-adic integers. We prove in the present paper that the category of polynomial functors from finitely generated free abelian groups to $\hat \Z_p$-modules of degree at most $p$ is equivalent to the category…

We study cocompleteness, co-wellpoweredness and generators in the centralizer category of an object or morphism in a monoidal category, and the center or the weak center of a monoidal category. We explicitly give some answers for when…

In this paper we prove that the subalgebras of cocommutative elements in the quantized coordinate rings of $M_{n}$, $GL_{n}$ and $SL_{n}$ are the centralizers of the trace $x_{1,1}+\dots+x_{n,n}$ in each algebra, for…

Let a real Lie group $G$ have a $C^\infty$ action on a real manifold $M$. Assume every nontrivial element of $G$ has nowhere dense fixpoint set in $M$. First, we show, in every frame bundle, except possibly the $0$th, that each stabilizer…

This work is devoted to computing the centralizer $Z (L)$ of an ordinary differential operator (ODO) in the ring of differential operators. Non-trivial centralizers are known to be coordinate rings of spectral curves and contain the ring of…

Let $D$ be division algebra over its center $C$, let $\sigma$ be an endormorphism of $D$, let $\delta$ be a left $\sigma$-derivation of $D$, and let $R=D[t;\sigma,\delta]$ be a skew polynomial ring. We study the structure of a class of…

This paper studies infinite acyclic complexes of finitely generated free modules over a commutative noetherian local ring $(R,m)$ with $m^3=0$. Conclusive results are obtained on the growth of the ranks of the modules in acyclic complexes,…

Let R be a ring and G a group. An R-module A is said to be artinian-by-(finite rank) if TorR(A) is artinian and A/TorR(A) has finite R-rank. The authors study ZG-modules A such that A/CA(H) is artinian-by-(finite rank) (as a Z-module) for…

P. Aluffi introduced in [1] a new graded algebra in order to conveniently express characteristic cycles in the theory of singular varieties. This algebra is attached to a surjective ring homomorphism $A\surjects B$ by taking a suitable…

For an extension A/B of neither necessarily associative nor necessarily unital rings, we investigate the connection between simplicity of A with a property that we call A-simplicity of B. By this we mean that there is no non-trivial ideal I…

Suppose $G$ is a $\mathcal{T}$-group (finitely generated torsion-free nilpotent) with centralizers outside of the derived subgroup being abelian of rank equal to $\text{rank}(Z_1)+1$. This includes the class of free nilpotent groups…