Related papers: Remarks on $K(1)$-local $K$-theory

Let p be an odd prime. Let K = Q(zeta) be the p-cyclotomic field. Let v be any primitive root mod p. Let sigma be a Q-isomorphism of K. Let P(sigma) = sigma^{p-2}v^{-(p-2)}+ ... + sigma v^{-1} +1 \in Z[G] where 1 \leq v^n \leq p-1 is a…

Lyubeznik conjectured that local cohomology modules of regular rings have finitely many associated primes. We examine this conjecture for polynomial rings over the integers, and record some equational identities that arise from studying…

Let $R$ be a commutative $k-$algebra over a field $k$. Assume $R$ is a noetherian, infinite, integral domain. The group of $k-$automorphisms of $R$,i.e.$Aut_k(R)$ acts in a natural way on $(R-k)$.In the first part of this article, we study…

Let $k$ be an algebraically closed field of characteristic 0, let $R$ be a commutative $k$-algebra, and let $M$ be a torsion free $R$-module of rank one with a connection $\nabla$. We consider the Lie-Rinehart cohomology with values in…

We apply the Schr\"odinger factorization method to the radial second-order equation for the relativistic Kepler-Coulomb problem. From these operators we construct two sets of one-variable radial operators which are realizations for the…

Using projective spaces as examples of toric manifolds, we examine K-theoretic fixed point localization. On the one hand, we will see how the permutation-equivariant theory of the point target space emerges as a necessary ingredient. On the…

Structural properties of unitary groups over local, not necessarily commutative, rings are developed, with applications to the computation of the orders of these groups (when finite) and to the degrees of the irreducible constituents of the…

We study the relative algebraic closure $K$ of $\bar{\mathbb{F}}_p((t))$ inside $\bar{\mathbb{F}}((t^{\mathbb{Q}}))$. We show that the supports of elements in $K$ have order type strictly less than $\omega^\omega$. We also recover a theorem…

A locally compact group $G$ is amenable if and only if it has Reiter's property $(P_p)$ for $p=1$ or, equivalently, all $p \in [1,\infty)$, i.e., there is a net $(m_\alpha)_\alpha$ of non-negative norm one functions in $L^p(G)$ such that…

This article studies the construction of Hopf algebras $H$ acting on a given algebra $K$ in terms of algebra morphisms $ \sigma \colon K \rightarrow \mathrm{M}_n(K)$. The approach is particularly suited for controlling whether these actions…

We compute rationally the topological (complex) K-theory of the classifying space BG of a discrete group provided that G has a cocompact G-CW-model for its classifying space for proper G-actions. For instance word-hyperbolic groups and…

We develop further the consequences of the irreducible-Boolean classification established in Ref. [9]; which have the advantage of allowing strong statistical calculations in disordered Boolean function models, such as the…

In this expositional paper, we discuss commutative algebra -- a study inspired by the properties of integers, rational numbers, and real numbers. In particular, we investigate rings and ideals, and their various properties. After, we…

This work concerns the Koszul complex $K$ of a commutative noetherian local ring $R$, with its natural structure as differential graded $R$-algebra. It is proved that under diverse conditions, involving the multiplicative structure of…

We consider the properties weak cancellation, K_1-surjectivity, good index theory, and K_1-injectivity for the class of extremally rich C*-algebras, and for the smaller class of isometrically rich C*-algebras. We establish all four…

In this paper, prime as well as primitive Kumjian-Pask algebras $\mathrm{KP}_R(\Lambda)$ of a row-finite $k$-graph $\Lambda$ over a unital commutative ring $R$ are completely characterized in graph-theoretic and algebraic terms. By applying…

Renault, Wassermann, Handelman and Rossmann (early 1980s) and Evans and Gould (1994) explicitly described the $K$-theory of certain unital AF-algebras $A$ as (quotients of) polynomial rings. In this paper, we show that in each case the…

We introduce filtered algebraic $K$-theory of a ring $R$ relative to a sublattice of ideals. This is done in such a way that filtered algebraic $K$-theory of a Leavitt path algebra relative to the graded ideals is parallel to the gauge…

In this paper we discuss physical derivations of the quantum K theory rings of symplectic Grassmannians. We compare to standard presentations in terms of Schubert cycles, but most of our work revolves around a proposed description in terms…

We develop an elementary theory of partially additive rings as a foundation of ${\mathbb F}_1$-geometry. Our approach is so concrete that an analog of classical algebraic geometry is established very straightforwardly. As applications, (1)…