Related papers: Algebraic redshift in the $C_2$-equivariant Adams …

Let $p$ be a prime, let $KU_p$ be $p$-complete complex $K$-theory, and let $\mathbb{Z}_p^\times$ denote the group of units in the $p$-adic integers. The $p$-adic Adams operations induce an action of the profinite group $\mathbb{Z}_p^\times$…

Circulant graphs $C_n(R)$ and $C_n(S)$ are said to be \emph{Adam's isomorphic} if there exist some $a\in \mathbb{Z}_n^*$ such that $S = a R$ under arithmetic reflexive modulo $n$. In 1970, Elspas and Turner \cite{eltu} raised a question on…

We provide a calculational method for rational stable equivariant homotopy theory for a torus G based on the homology of the Borel construction on fixed points. More precisely we define an abelian torsion model, A_t(G) of finite injective…

The Adams operators $\Psi_n$ on a Hopf algebra $H$ are the convolution powers of the identity of $H$. We study the Adams operators when $H$ is graded connected. They are also called Hopf powers or Sweedler powers. The main result is a…

Let E be an operator algebra on a Hilbert space with finite-dimensional generated C*-algebra. A classification is given of the locally finite algebras and the operator algebras obtained as limits of direct sums of matrix algebras over E…

Given a commutative ring spectrum $R$ let $\Lambda_XR$ be the Loday functor constructed by Brun, Carlson and Dundas. Given a prime $p\geq 5$ we calculate $\pi_*(\Lambda_{S^n}H\mathbb{F}_p)$ and $\pi_*(\Lambda_{T^n}H\mathbb{F}_p)$ for $n\leq…

We develop and collect techniques for determining Hochschild cohomology of skew group algebras S(V)#G and apply our results to graded Hecke algebras. We discuss the explicit computation of certain types of invariants under centralizer…

We establish a version of Kn\"{o}rrer's Periodicity Theorem in the context of noncommutative invariant theory. Namely, let $A$ be a left noetherian AS-regular algebra, let $f$ be a normal and regular element of $A$ of positive degree, and…

We show that the braided tensor product algebra $A_1\underline{\otimes}A_2$ of two module algebras $A_1, A_2$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $A_1$ with a subalgebra of…

We compute the two-cocycles (or multipliers) of the free nilpotent groups of class $2$ and rank $n$ and give conditions for simplicity of the corresponding twisted group $C^*$-algebras. These groups are representation groups for…

In this paper, motivated by the Berger, Coburn and Lebow and Bercovici, Douglas and Foias theory for tuples of commuting isometries, we study analytic representations and joint invariant subspaces of a class of commuting $n$-isometries and…

The mod 2 Moore spectrum $C(2)$ is the cofiber of the self-map $2: \mathbb{S} \to \mathbb{S}$. Building on work of Burklund, Hahn, and Senger, we prove that above a line of slope $\frac{1}{5}$, the Adams spectral sequence for $C(2)$…

We prove the Gromov-Lawson-Rosenberg Conjecture for the group Z/4xZ/4 by computing the connective real k-homology of the classifying space with the Adams spectral sequence and two types of detection theorems for the kernel of the alpha…

We consider a class of C*-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner's Toeplitz algebras. By exhibiting a homotopy of…

Let $\Gamma=(\mathcal{V},\mathcal{E})$ be a graph, whose vertices $v\in \mathcal{V}$ are colored black and white and labeled with invertible elements $\lambda_v$ from a commutative and associative ring $R$ containing $\pm 1$. Then we…

Localized at almost all primes, we describe the structure of differentials in several important spectral sequences that compute the cohomology of classifying spaces of topological Kac-Moody groups. In particular, we show that for all but a…

We describe a deformation of the $\infty$-category of Borel $G$-spectra for a finite group $G$. This provides a new presentation of the $a$-complete real Artin--Tate motivic stable homotopy category when $G=C_2$ and gives a new…

We compute some R-motivic stable homotopy groups. For $s - w \leq 11$, we describe the motivic stable homotopy groups $\pi_{s,w}$ of a completion of the R-motivic sphere spectrum. We apply the $\rho$-Bockstein spectral sequence to obtain…

An algebra $V$ with a cross product $\times$ has dimension 3 or 7. In this work, we use 3-tangles to describe, and provide a basis for, the space of homomorphisms from $V^{\otimes n}$ to $V^{\otimes m}$ that are invariant under the action…

We present progress in trying to verify a long-standing conjecture by Mark Mahowald on the $v_{1}$-periodic component of the classical Adams spectral sequence for a Moore space $M$. The approach we follow was proposed by John Palmieri in…