Related papers: Noncommutative Noether's problem is almost equival…

We study the critical Neumann problem \begin{equation*} \begin{cases} -\Delta u = |u|^{2^*-2}u &\text{in }\Sigma_\omega,\\ \quad\frac{\partial u}{\partial\nu}=0 &\text{on }\partial\Sigma_\omega, \end{cases} \end{equation*} in the unbounded…

In recent years, researchers have discovered various large algebraic structures that have surprising finiteness properties, such as FI-modules and Delta-modules. In this paper, we add another example to the growing list: we show that…

Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…

We extend the Gelfand-Naimark duality of commutative C*-algebras, "A COMMUTATIVE C*-ALGEBRA -- A LOCALLY COMPACT HAUSDORFF SPACE" to "A C*-ALGEBRA--A QUOTIENT OF A LOCALLY COMPACT HAUSDORFF SPACE". Thus, a C*-algebra is isomorphic to the…

Let $A$ be a nondegenerate dimer (or ghor) algebra on a torus, and let $Z$ be its center. Using cyclic contractions, we show the following are equivalent: $A$ is noetherian; $Z$ is noetherian; $A$ is a noncommutative crepant resolution;…

The Noether procedure carries an inherent ambiguity due to the necessary local extension, no longer a symmetry, of the global symmetry. The gauging should fix the ambiguity once and for all, however, and, for translations, the general…

This paper presents a new Lie theoretic approach to fractal calculus, which in turn yields such new results as a Fractal Noether's Theorem, a setting for fractal differential forms, for vector fields, and Lie derivatives, as well as…

Recently, an extension of the standard four-dimensional scalar conformal action, yielding a second-order field equation that remains conformally invariant, was proposed. In spite of this, the corresponding action is not invariant under…

We prove a skew generalization of the Newton-Puiseux theorem for the field $F = \bigcup_{n=1}^\infty \mathbb{C}((x^\frac{1}{n}))$ of Puiseux series: For any positive real number $\alpha$, we consider the $\mathbb{C}$-automorphism $\sigma$…

We prove that any countable discrete and torsion free subgroup of a general linear group over an arbitrary field or a similar subgroup of an almost connected Lie group satisfies the integral algebraic K-theoretic (split) Novikov conjecture…

The aim of the paper is to attach a noncommutative cluster-like structure to each marked surface $\Sigma$. This is a noncommutative algebra ${\mathcal A}_\Sigma$ generated by "noncommutative geodesics" between marked points subject to…

In this paper, we formulate and prove a version of the Stone-von Neumann Theorem for every $ C^{\ast} $-dynamical system of the form $ (G,\mathbb{K}(\mathcal{H}),\alpha) $, where $ G $ is a locally compact Hausdorff abelian group and $…

We establish a new no-go theorem for cosmology: spatially flat ($k=0$) and open ($k=-1$) Friedmann--Robertson--Walker (FRW) non-static spacetimes cannot be simultaneously nonsingular, geodesically complete, and consistent with the averaged…

We resolve an open question posed by the authors of arXiv:1501.06925v2 in 2015 concerning a Gr\"obner theoretic approach for the noetherianity of the twisted commutative algebra ${\rm Sym}({\rm Sym}^2(\mathbf{C}^\infty))$. We provide a…

Given a circle-valued Morse function of a closed oriented manifold, we prove that Reidemeister torsion over a non-commutative formal Laurent polynomial ring equals the product of a certain non-commutative Lefschetz-type zeta function and…

Studying the general structure of the noncommutative (NC) local groups, we prove a no-go theorem for NC gauge theories. According to this theorem, the closure condition of the gauge algebra implies that: 1) the local NC $u(n)$ {\it algebra}…

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)…

Let G be a reductive connected linear algebraic group over an algebraically closed field of positive characteristic and let g be its Lie algebra. First we extend a well-known result about the Picard group of a semisimple group to reductive…

In 1955 Dye proved that two von Neumann factors not of type I_2n are isomorphic (via a linear or a conjugate linear *-isomorphism) if and only if their unitary groups are isomorphic as abstract groups. We consider an analogue for…

Let Q be a finite quiver without oriented cycles, let \Lambda be the associated preprojective algebra, let g be the associated Kac-Moody Lie algebra with Weyl group W, and let n be the positive part of g. For each Weyl group element w, a…