Related papers: The upper bound for the index of nilpotency for a …

The authors here show that the partition $P_{k,l}(Q)$ in the table $\mathcal T(Q)$ of partitions having maximal nilpotent commutator a given stable partition $Q$, defined in [IKVZ2], is identical to the analogous partition $P_{k,l}^Q$…

We show that every self--adjoint matrix B of trace 0 can be realized as B=T+T^* for a nilpotent matrix T of norm no greater than K times the norm of B, for a constant K that is independent of matrix size. More particularly, if D is a…

We study the commuting graph of $n\times n$ matrices over the field of $p$-adics $\mathbb{Q}_p$, whose vertices are non-scalar $n\times n$ matrices with entries in $\mathbb{Q}_p$ and whose edges connect pairs of matrices that commute under…

We study Jacobi matrices with $N$-periodically modulated recurrence coefficients when the sequence of $N$-step transfer matrices is convergent to a non-trivial Jordan block. In particular, we describe asymptotic behavior of their…

There are normal sub-blocks of nilpotent blocks which are NOT nilpotent or, equivalently, nilpotent extensions of non-nilpotent blocks. In this paper we determine the source algebra structure of the non-nilpotent blocks involved in these…

For a given reciprocal matrix A, we give a union of matrix intervals in which any consistent matrix obtained from an efficient vector for A lies, and, conversely, any consistent matrix in this union comes from an efficient vector for A. The…

We discuss multi-graded nilpotent tuples of multi-graded vector spaces which are a generalization of graded nilpotent pairs. The multi-grading yields a natural notion of a shape of such tuple and our main interest is to answer the question…

We establish bounds on the mixing times of conjugacy-invariant random walks on finite nilpotent groups in terms of the mixing times of their projections onto the abelianization. This comparison framework shows that, in several natural cases…

This paper gives a combinatorial description of the set of irreducible components of the semistable locus of the global nilpotent cone, in genus $\ge2$. The first main result of this paper states that the set of irreducible components of…

The main result of this paper is the following: if F is any field and R is any F-subalgebra of the algebra of nxn matrices over F with Lie nilpotence index m, then the F-dimension of R is less or equal than M(m+1,n), where M(m+1,n) is the…

Let $A$ be a finite dimensional representation-finite algebra over an algebraically closed field. The aim of this work is to generalize the results proven in CGS. Precisely, we determine which vertices of $Q_A$ are sufficient to be…

We obtain general upper bounds of the sizes and the numbers of Jordan blocks for the eigenvalues $\lambda \not= 1$ in the monodromies at infinity of polynomial maps.

Let $M_n$ denote the algebra of $n \times n$ complex matrices and let $\mathcal{A}\subseteq M_n$ be an arbitrary structural matrix algebra, i.e. a subalgebra of $M_n$ that contains all diagonal matrices. We consider injective maps $\phi :…

We develop the theory of the higher commutator for Taylor varieties. A new higher commutator operation called the hypercommutator is defined using a type of invariant relation called a higher dimensional congruence. The hypercommutator is…

A maximum modulus estimate for the nonstationary Stokes equations in $C^2$ domain is found. The singular part and regular part of Poisson kernel are analyzed. The singular part consists of the gradient of single layer potential and the…

In this paper, we determine the structure of the nilpotent multipliers of all pairs $(G,N)$ of finitely generated abelian groups where $N$ admits a complement in $G$. Moreover, some inequalities for the nilpotent multipliers of pairs of…

In this article, we introduce the concept of nilpotent graph of a finite commutative ring. The set of all non nilpotent elements of a ring is taken as the vertex set and two vertices are adjacent if and only if their sum is nilpotent. We…

Let $M_n(\mathbb{F})$ be the algebra of $n \times n$ matrices over a field $\mathbb{F}$ of characteristic not equal to $2$. If $n\ge 2$, we show that an arbitrary map $\phi : M_n(\mathbb{F}) \to M_n(\mathbb{F})$ is Jordan multiplicative,…

Fix a field F. A zero-nonzero pattern A is said to be potentially nilpotent over F if there exists a matrix with entries in F with zero-nonzero pattern A that allows nilpotence. In this paper we initiate an investigation into which…

The aim of this work is to find some exact sequences on the $c$- nilpotent multiplier of a group $G$. We also give an upper bound for the $c$- nilpotent multiplier of finite $p$-groups and give the explicit structure of groups whose take…