Related papers: Algebraic shifting and exterior and symmetric alge…
We compare various viewpoints on down-sets (simplicial complexes), illustrating how the combinatorial inclusion-exclusion principle may serve as an alternative to more advanced methods of studying their face numbers.
This paper does not contain any new results, it is just an attempt to present, in a systematic way, one construction which establishes an interesting relationship between some ideas and notions well-known in the theory of integrable systems…
Five algebraic notions of termination are formalised, analysed and compared: wellfoundedness or Noetherity, L\"ob's formula, absence of infinite iteration, absence of divergence and normalisation. The study is based on modal semirings,…
It is shown that to every Q-linear cycle \bar\alpha modulo numerical equivalence on an abelian variety A there is canonically associated a Q-linear cycle \alpha modulo rational equivalence on A lying above \bar\alpha. The assignment…
In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…
We construct two bases for each cluster algebra coming from a triangulated surface without punctures. We work in the context of a coefficient system coming from a full-rank exchange matrix, for example, principal coefficients.
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
After summarizing basic concepts for the exterior algebra we firstly discuss the gauge structure of the bundle over base manifold for deciding the form of the gravitational sector of the total Lagrangian in any dimensions. Then we couple…
When $A = \mathbb{k}[x_1, \ldots, x_n]$ and $G$ is a small subgroup of $\operatorname{GL}_n(\mathbb{k})$, Auslander's Theorem says that the skew group algebra $A \# G$ is isomorphic to $\operatorname{End}_{A^G}(A)$ as graded algebras. We…
First, we prove an algebraization result for rig-smooth algebras over a general noetherian ring; this positively answers the question raised in [Sta24, Tag 0GAX]. Then we prove a general partial algebraization result in non-archimedean…
Since the invention of space-time coding numerous algebraic methods have been applied in code design. In particular algebraic number theory and central simple algebras have been on the forefront of the research. In this paper we are turning…
The set theory relations \in, \backslash, \Delta, \cap, and \cup have corollaries in subspace relations. Geometric Algebra is introduced as the ideal framework to explore these subspace operations. The relations \in, \backslash, and \Delta…
In this paper we present three different results dealing with the number of $(\leq k)$-facets of a set of points: 1. We give structural properties of sets in the plane that achieve the optimal lower bound $3\binom{k+2}{2}$ of $(\leq…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
We describe a grading switching for arbitrary non-associative algebras of prime characteristic p, aimed at producing a new grading of an algebra from a given one. This is inspired by a fundamental tool in the classification theory of…
Given a central simple algebra with involution over an arbitrary field, \'etale subalgebras contained in the space of symmetric elements are investigated. The method emphasizes the similarities between the various types of involutions and…
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…
We use the exterior product of double forms to reformulate celebrated classical results of linear algebra about matrices and bilinear forms namely the Cayley-Hamilton theorem, Laplace expansion of the determinant, Newton identities and…
An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut
Based on a theorem by Vasconcelos, we give an algorithm for equidimensional decomposition of algebraic sets using syzygy computations via Gr\"obner bases. This algorithm avoids the use of elimination, homological algebra and processing the…