In Kapranov, M. Noncommutative geometry based on commutator expansions, J. reine angew. Math 505 (1998) 73-118, a theory of noncommutative algebraic varieties was proposed. Here we prove a structure theorem for the ...

We present a characterization of states in generalized probabilistic models by appealing to a non-commutative version of geometric probability theory based on algebraic geometry techniques. Our theoretical framework allows ...

In this paper we present a survey of some algebraic characterizations of Hilbert’s Nullstellensatz for non-commutative rings of polynomial type. Using several results established in the literature, we obtain a version of ...

We follow the main idea of  A. Connes for the construction of a metric in the state space of a C*-algebra. We focus in the reduced algebra of a discrete group Г, and prove some equivalences and relations between two central ...

We study 2-cocycle twists, or equivalently Zhang twists, of semigroup algebras over a field k. If the underlying semigroup is affine, that is abelian, cancellative and finitely generated, then Spec k[S] is an affine toric ...

In this article we considered models of particles living in a three-dimensional space-time with a nonstandard noncommutativity induced by shifting canonical coordinates and momenta with generators of a unitary irreducible ...

We show that certain homological regularity properties of graded connected algebras, such as being AS-Gorenstein or AS-Cohen–Macaulay, can be tested by passing to associated graded rings. In the spirit of noncommutative ...

A fundamental aspect of the quantum-to-classical limit is the transition from a non-commutative algebra of observables to commutative one. However, this transition is not possible if we only consider unitary evolutions. ...