Related papers: Another invariant for AT actions

We argue here that, as it happens in Classical and Quantum Mechanics, where it has been proven that alternative Hamiltonian descriptions can be compatible with a given set of equations of motion, the same holds true in the realm of…

The first part deals with piecewise fractional linear maps with three branches. Given a map $T$ a map $S$ is called a related map if some branches of $T$ are replaced by a 'flipped' branch, namely a branch of $1-T$. The main question is if…

In this work, for a given inverse semigroup we will define the crossed product of an inverse semigroup by a partial action. Also, we will associate to an inverse semigroup $G$ an inverse semigroup $S_G$, and we will prove that there is a…

We construct a projective variety with discrete, non-finitely generated automorphism group. As an application, we show that there exists a complex projective variety with infinitely many non-isomorphic real forms.

An alternative construction, using Witt's formalism, of the Arf-invariant of quadratic forms in characteristic 2.

We investigate the transfer of the Cohen-Macaulay property from a commutative ring to a subring of invariants under the action of a finite group. Our point of view is ring theoretic and not a priori tailored to a particular type of group…

In the present paper the field of invariants of the adjoint action of the unitriangular group in the nilradical of any parabolic subalgebra is described.

We show that if a nontrivial group admits a locally invariant ordering, then it admits uncountably many locally invariant orderings. For the case of a left-orderable group, we provide an explicit construction of uncountable families of…

In this paper we classify invariant noncommutative connections in the framework of the algebra of endomorphisms of a complex vector bundle. It has been proven previously that this noncommutative algebra generalizes in a natural way the…

We give a sufficient condition for a symbolic topological dynamical system with action of a countable amenable group to be an extension of the full shift, a problem analogous to those studied by Ashley, Marcus, Johnson and others for…

Two types of recurrence sets are introduced for inverse semigroup partial actions in topological spaces. We explore their connections with similar notions for related types of imperfect symmetries (prefix inverse semigroup expansions,…

In the previous article we introduced the new concept of mixed representations of quivers and described the generators of their algebras of invariants. In this article we describe the defining relations of these algebras. Some applications…

We define the notion of an invariant function on a cluster ensemble with respect to an action of the cluster modular group on its associated function fields. We realize many examples of previously studied functions as elements of this type…

We study model theory of actions of finite groups on substructures of a stable structure. We give an abstract description of existentially closed actions as above in terms of invariants and PAC structures. We show that if the corresponding…

These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…

We consider the problem of extending an acyclic binary relation that is invariant under a given family of transformations into an invariant preference. We show that when a family of transformations is commutative, every acyclic invariant…

This paper studies separating invariants: mappings on $D$ dimensional domains which are invariant to an appropriate group action, and which separate orbits. The motivation for this study comes from the usefulness of separating invariants in…

Let $\mathcal{A}=(A_{1},...,A_{n},...)$ be a finite or infinite sequence of $2\times2$ matrices with entries in an integral domain. We show that, except for a very special case, $\mathcal{A}$ is (simultaneously) triangularizable if and only…

We describe a collection of computer scripts written in PARI/GP to compute, for reflection groups determined by finite-volume polyhedra in $\mathbb{H}^3$, the commensurability invariants known as the invariant trace field and invariant…

We describe isomorphisms of groups of several periodic infinite matrices and isomorphisms of groups of invertible elements of unital locally matrix algebras.