Related papers: Stability index for algebras with involution

We prove a stability theorem for families of holomorphically-parallelizable manifolds in the category of Hermitian manifolds.

The category of Frobenius Lie algebras is stable under deformation, and here we examine explicit infinitesimal deformations of four and six dimensional Frobenius Lie algebras with the goal of understanding if the spectrum of a Frobenius Lie…

The paper deals with $\Sigma-$composition and $\Sigma$-essential composition of terms, which lead to stable and s-stable varieties of algebras. A full description of all stable varieties of semigroups, commutative and idempotent groupoids…

A commutative ring $R$ is stable if every non-zero ideal $I$ of $R$ is projective over its ring of endomorphisms. Motivated by a paper of Bass in the 1960s, stable rings have received wide attention in the literature ever since then. Much…

Evolution algebras are a special class of non-associative algebras exhibiting connections with different fields of Mathematics. Hilbert evolution algebras generalize the concept through a framework of Hilbert spaces. This allows to deal…

We study invariant Hermitian forms on a conformal vertex algebra and on their (twisted) modules. We establish existence of a non-zero invariant Hermitian form on an arbitrary $W$-algebra. We show that for a minimal simple $W$-algebra…

Let $H$ be a connected Hopf algebra acting on an algebra $A$. Working over a base field having characteristic $0$, we show that for a given prime (semi-prime, completely prime) ideal $I$ of $A$, the largest $H$-stable ideal of A contained…

The space of derivations of finite dimensional evolution algebras associated to graphs over a field with characteristic zero has been completely characterized in the literature. In this work we generalize that characterization by describing…

Motivated by the ubiquitous sampled-data setup in applied control, we examine the stability of a class of difference equations that arises by sampling a right- or left-invariant flow on a matrix Lie group. The map defining such a difference…

The stability of topological persistence is one of the fundamental issues in topological data analysis. Numerous methods have been proposed to address the stability of persistent modules or persistence diagrams. Recently, the concept of…

We define antidomain operations for algebras of multiplace partial functions. For all signatures containing composition, the antidomain operations and any subset of intersection, preferential union and fixset, we give finite equational or…

Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…

We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…

We analyze stable homology over associative rings and obtain results over Artin algebras and commutative noetherian rings. Our study develops similarly for these classes; for simplicity we only discuss the latter here. Stable homology is a…

We prove that the algebra of invariants of a complete path algebra under the action of a homogeneous group of continuous algebra automorphisms is a complete path algebra and preserves finite or tame representation type.

We study several different notions of algebraicity in use in stable homotopy theory and prove implications between them. The relationships between the different meanings of algebraic are unexpectedly subtle, and we illustrate this with…

We generalize signature Gr\"obner bases, previously studied in the free algebra over a field or polynomial rings over a ring, to ideals in the mixed algebra $R[x_1,...,x_k]\langle y_1,\dots,y_n \rangle$ where $R$ is a principal ideal…

The u-invariant of a field is the supremum of the dimensions of anisotropic quadratic forms over the field. We define corresponding u-invariants for hermitian and generalised quadratic forms over a division algebra with involution in…

As is known, every finite-dimensional algebra over a field is isomorphic to the centralizer algebra of \textbf{two} matrices. So it is fundamental to study first the centralizer algebra of a single matrix, called a centralizer matrix…

In this paper we study stable finiteness of ample groupoid algebras with applications to inverse semigroup algebras and Leavitt path algebras, recovering old results and proving some new ones. In addition, we develop a theory of (faithful)…