Related papers: Unified computational approach to nilpotent algebr…

Leibniz superalgebras with nilindex $n + m$ and characteristic sequence $(n-1, 1 \ | \ m)$ divided into four parametric classes that contain a set of non-isomorphic superalgebras. In this paper, we give a complete classification of solvable…

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…

Let $k$ be a field of any characteristic, $V$ a finite-dimensional vector space over $k$, and $S^d(V^*)$ be the $d$-th symmetric power of the dual space $V^*$. Given a linear map $\varphi$ on $V$ and an eigenvector $w$ of $\varphi$, we…

This paper is devoted to the study of graded associative algebras that satisfy a graded polynomial identity of degree $2$. % Let $\mathsf{G}$ be a finite abelian group, $\mathbb{F}$ a field of characteristic zero and $\mathfrak{A}$ a…

This thesis gives an overview of the state-of-the-art randomized linear algebra algorithms for singular value decomposition (SVD), including the presentation of existing pseudo-codes and theoretical error analysis. Our main focus is on…

In this paper we investigate locally nilpotent derivations on the polynomial algebra in three variables over a field of characteristic zero. We introduce an iterating construction giving all locally nilpotent derivations of rank $2$. This…

Convergence is a crucial issue in iterative algorithms. Damping is commonly employed to ensure the convergence of iterative algorithms. The conventional ways of damping are scalar-wise, and either heuristic or empirical. Recently, an…

Nonuniform Deterministic Finite Automata (NUDFA) over monoids were invented by Barrington to study boundaries of nonuniform constant-memory computation. Later, results on these automata helped to indentify interesting classes of groups for…

A Riemannian Einstein solvmanifold (possibly, any noncompact homogeneous Einstein space) is almost completely determined by the nilradical of its Lie algebra. A nilpotent Lie algebra, which can serve as the nilradical of an Einstein metric…

We investigate the filtration corresponding to the degree function induced by a non-zero locally nilpotent derivation and its associated graded algebra. We show that this kind of filtration, referred to as the LND-filtration, is the ideal…

We characterize those nilpotent algebras of prime power order and finite type in congruence modular varieties that have infinitely many polynomially inequivalent congruence preserving expansions.

We give a Clifford correspondence for an algebra A over an algebraically closed field, that is an algorithm for constructing some finite-dimensional simple A-modules from simple modules for a subalgebra and endomorphism algebras. This…

We develop a theory of multigraded (i.e., $N^l$-graded) combinatorial Hopf algebras modeled on the theory of graded combinatorial Hopf algebras developed by Aguiar, Bergeron, and Sottile [Compos. Math. 142 (2006), 1--30]. In particular we…

All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always…

Let $G$ be a connected complex reductive algebraic group with Lie algebra $\mathfrak{g}$. The Lusztig--Vogan bijection relates two bases for the bounded derived category of $G$-equivariant coherent sheaves on the nilpotent cone…

In this note we present some experimental results on the general matrix nilpotent Lie algebras derived by calculations on a computer

The complexity of the equation solvability problem is known for nilpotent groups, for not solvable groups and for some semidirect products of Abelian groups. We provide a new polynomial time algorithm for deciding the equation solvability…

The paper is devoted to give the complete algebraic classification of nilpotent binary Lie algebras of dimension $\leq 6$ over an arbitrary base field ${\mathbb{F}}$ of characteristic not $2$ and the complete geometric classification of…

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…

The singular value decomposition (SVD) allows to write a matrix as a product of a left singular vectors matrix, a nonnegative singular values diagonal matrix and a right singular vectors matrix. Among the applications of the SVD are the…