Related papers: Noncommutative localization in group rings
We aim to construct a non-commutative algebraic geometry by using generalised valuations. To this end, we introduce groupoid valuation rings and associate suitable value functions to them. We show that these objects behave rather like their…
We study the Duflot filtration on the Borel equivariant cohomology of smooth manifolds with a smooth $p$-torus action. We axiomatize the filtration and prove analog of several structural results about equivariant cohomology rings in this…
We prove a division algorithm for group rings of high genus surface groups and use it to show that some $2$-complexes with surface fundamental groups are standard. We also give an application of division to cohomological dimension of…
We classify generic coadjoint orbits for symplectomorphism groups of compact symplectic surfaces with or without boundary. We also classify simple Morse functions on such surfaces up to a symplectomorphism.
In the last few years several new Random Matrix Models have been proposed and studied. They have found application in various different contexts, ranging from the physics of mesoscopic systems to the chiral transition in lattice gauge…
A method for the deformation quantization of coadjoint orbits of semisimple Lie groups is proposed. It is based on the algebraic structure of the orbit. Its relation to geometric quantization and differentiable deformations is explored.
This paper considers a generalisation of the idea of a Hopf algebra in which a commutative ring replaces the field in the unit and counit. It is motivated by an example from the inverse scattering formalism for solitons. We begin with the…
We explain how to exploit Rost's theory of Chow groups with coefficients to carry some computations of cohomological invariants (i.e. characteristic classes for G-torsors in Galois cohomology, for an algebraic group G). In particular, we…
Modern coaxial and planar HPGe detectors allow a precise determination of the energies and trajectories of the impinging gamma-rays. This entails the location of the gamma interactions inside the crystal from the shape of the delivered…
In this paper we study generalized Gorenstein Arf rings; a class of one-dimensional Cohen-Macaulay local Arf rings that is strictly contained in the class of Gorenstein rings. We obtain new characterizations and examples of Arf rings, and…
In this work, we generalize several topological results and concepts from ring theory to the setting of monoids.
A method is proposed to employ entangled and squeezed light for determining the position of a party and for synchronizing distant clocks. An accuracy gain over analogous protocols that employ classical resources is demonstrated and a…
In this paper we use formal group rings to construct an algebraic model of the $T$-equivariant oriented cohomology of smooth toric varieties. Then we compare our model with known results of equivariant cohomology of toric varieties to…
This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric…
One of the most useful methods for studying the stable homotopy category is localising at some spectrum E. For an arbitrary stable model category we introduce a candidate for the E-localisation of this model category. We study the…
We provide the localization procedure for monoidal categories by a real commuting family of braiders. For an element $w$ of the Weyl group, $\mathscr{C}_w$ is a subcategory of modules over quiver Hecke algebra which categorifies the quantum…
We describe how orbital graphs can be used to improve the practical performance of many algorithms for permutation groups, including intersection and stabilizer problems. First we explain how orbital graphs can be integrated in partition…
We explore the connection between ring homomorphisms and semigroup homomorphisms on matrix algebras over rings or $C^*$-algebras.
This paper is devoted to present some characterizations for a local ring to be generically Gorenstein and Gorenstein by means of $\delta$-invariant and linkage theory.
This is a survey of noncommutative generalizations of the spectrum of a ring, written for the Notices of the American Mathematical Society.