Related papers: The strong nilpotency index of a matrix

The paper studies nilpotent $n$-Lie superalgebras. More specifically speaking, we first prove Engel's theorem for $n$-Lie superalgebras. Second, we research some properties of nilpotent $n$-Lie superalgebras, Finally, we give several…

It is shown that any finite-dimensional homomorphic image of an inverse limit of nilpotent not-necessarily-associative algebras over a field is nilpotent. More generally, this is true of algebras over a general commutative ring k, with…

We describe isomorphisms between strongly triangular matrix rings that were defined earlier in Berkenmeier et al. (2000) as ones having a complete set of triangulating idempotents, and we show that the so-called triangulating idempotents…

The paper studies algebraic strong shift equivalence of matrices over $n$-variable polynomial rings over a principal ideal domain $D$($n\leq 2$). It is proved that in the case $n=1$, every non-zero matrix over $D[x]$ has a full rank…

We classify the nilpotent Lie algebras of real dimension eight and minimal center that admit a complex structure. Furthermore, for every such nilpotent Lie algebra $\mathfrak{g}$, we describe the space of complex structures on…

The index of a Lie algebra is an important invariant which arises in several areas, e.g. in the study of coadjoint orbits for a Lie group, in invariant theory and in representation theory. We study the index for several classes of nilpotent…

In this paper we describe geometry of orbits of upper triangular matrices of nilpotent order 2 under conjugation by the group of upper triangular invertible matrices in terms of link patterns. Further we apply this description to the…

We describe a procedure to attach a nilpotent strong homotopy Lie algebra to every simple hypergraph and prove that two hypergraphs are isomorphic if and only if the corresponding strong homotopy Lie algebras are isomorphic. As an…

In this paper, we study nilpotent structures of an oriented vector bundle $E$ of rank $4n$ with a neutral metric $h$ and an $h$-connection $\nabla$. We define $H$-nilpotent structures of $(E, h, \nabla )$ for a Lie subgroup $H$ of $SO(2n,…

In this paper we investigate nilpotenct and probabilistically nilpotent Hopf algebras. We define nilpotency via a descending chain of commutators and give a criterion for nilpotency via a family of central invertible elements. These…

There are some results on nilpotent Lie algebras $ L $ investigate the structure of $ L $ rely on the study of its $2$-nilpotent multiplier. It is showed that the dimension of the $2$-nilpotent multiplier of $ L $ is equal to $ \frac{1}{3}…

We consider second-order partial differential operators $H$ in divergence form on $\Ri^d$ with a positive-semidefinite, symmetric, matrix $C$ of real $L_\infty$-coefficients and establish that $H$ is strongly elliptic if and only if the…

A (vector space) basis B of a Lie algebra is said to be very nilpotent if all the iterated brackets of elements of B are nilpotent. In this note, we prove a refinement of Engel's Theorem. We show that a Lie algebra has a very nilpotent…

We provide a nilpotency criterion for fusion systems in terms of the vanishing of its cohomology with twisted coefficients.

Supernilpotence is a generalization of nilpotence using a recently developed theory of higher-arity commutators for universal algebras. Many important structural properties have been shown to be associated with supernilpotence, and the…

This paper explores the properties of multiplicative Lie algebra structures on a nilpotent group of class $2$. We also present a method for determining a multiplicative Lie algebra structure on a group that serves as an extension of one Lie…

In the paper, we first classify all polynomial maps $H$ of the following form: $H=\big(H_1(x_1,x_2,\ldots,x_n),H_2(x_1,x_2),H_3(x_1,x_2),\ldots,H_n(x_1,x_2)\big)$ with $JH$ nilpotent. After that, we generalize the structure of $H$ to…

We develop a structure theory for nilpotent symplectic alternating algebras. We then give a classification of all nilpotent symplectic alternating algebras of dimension up to 10 over any field. The study reveals a new subclasses of powerful…

We establish combinatorial formulas for the index of a class of matrix Lie algebras whose matrix forms are encoded by strict partial orderings.

We establish a version of a semistable reduction theorem over a log point with a non-trivial nilpotent structure. In order to do this we extend the classical desingularization theories to non-reduced schemes with generically principal…