Related papers: Unified computational approach to nilpotent algebr…

Any finite-dimensional commutative (associative) graded algebra with all nonzero homogeneous subspaces one-dimensional is defined by a symmetric coefficient matrix. This algebraic structure gives a basic kind of $A$-graded algebras…

A nilpotent quotient algorithm for finitely presented Lie rings over Z (LieNQ) is described. The paper studies graded and non-graded cases separately. The algorithm computes the so-called nilpotent presentation for a finitely presented,…

The parameter coclass has been used successfully in the study of nilpotent algebraic objects of different kinds. In this paper a definition of coclass for nilpotent semigroups is introduced and semigroups of coclass 0, 1, and 2 are…

We study finite-dimensional nonassociative algebras. We prove the implicit function theorem for such algebras. This allows us to establish a correspondence between such algebras and quasigroups, in the spirit of classical correspondence…

Taking into account the theoretical results and guidelines given inthis work, we introduce a computational method to construct any 2 step nilpotent quadratic algebra of d generators. Along the work we show that the key of the classification…

This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…

The class of associative trialgebras, also known as triassociative algebras, is characterized by three multiplications and eleven relations that generalize associativity. In the current paper, we present a study of nilpotent triassociative…

We study algebraic algorithms for expressing the number of non-negative integer solutions to a unimodular system of linear equations as a function of the right hand side. Our methods include Todd classes of toric varieties via Gr\"obner…

We give a classification of 5- and 6-dimensional complex one-generated nilpotent Novikov algebras

{\sc CLIFFORD} is a Maple package for computations in Clifford algebras $\cl (B)$ of an arbitrary symbolic or numeric bilinear form B. In particular, B may have a non-trivial antisymmetric part. It is well known that the symmetric part g of…

This article surveys results on graded algebras and their Hilbert series. We give simple constructions of finitely generated graded associative algebras $R$ with Hilbert series $H(R,t)$ very close to an arbitrary power series $a(t)$ with…

To a higher rank directed graph $(\Lambda, d)$, in the sense of Kumjian and Pask, one can associate natural noncommutative analytic Toeplitz algebras, both weakly closed and norm closed. We introduce methods for the classification of these…

In this paper we study subalgebras of complex finite dimensional evolution algebras. We obtain the classification of nilpotent evolution algebras whose any subalgebra is an evolution subalgebra with a basis which can be extended to a…

In this paper we extend categorically the notion of a finite nilpotent group to fusion categories. To this end, we first analyze the trivial component of the universal grading of a fusion category C, and then introduce the upper central…

We take new algebraic and geometric perspectives on the old subject of SQCD. We count chiral gauge invariant operators using generating functions, or Hilbert series, derived from the plethystic programme and the Molien-Weyl formula. Using…

We describe the E-infinity algebra structure on the complex of singular cochains of a topological space, in the context of sheaf theory. As a first application, for any algebraic variety we define a weight filtration compatible with its…

We apply results from the geometry of nilpotent orbits and nilpotent Slodowy slices, together with modularity and asymptotic analysis of characters, to prove many new isomorphisms between affine W-algebras and affine Kac-Moody vertex…

Let $\mathbf{A}$ be a finite nilpotent algebra in a congruence modular variety with finitely many fundamental operations. If $\mathbf{A}$ is of prime power order, then it is known that there is a polynomial $p$ such that for every $n \in…

In this paper we classify solvable Leibniz algebras whose nilradical is a null-filiform algebra. We extend the obtained classification to the case when the solvable Leibniz algebra is decomposed as a direct sum of its nilradical, which is a…

We give an estimate of the number $N(\lambda)$ of eigenvalues $<\lambda$ for the image under an irreducible representation of the ``sublaplacian'' on a stratified nilpotent Lie algebra. We also give an estimate for the trace of the…