Related papers: Test Groups for Whitehead Groups

Let W be a Weyl group. We can define the notion of positivity of a W-module in terms of the corresponding module over the asymptotic Iwahori-Hecke algebra. We state a conjecture which says that certain explicit W-modules are positive and we…

We consider the problem of existence of representations of topological groupoids on a principal bundle and the classification of such representations up to gauge transformation. Such representations naturally occur in various contexts such…

We study a composition operation on monads, equivalently presented as large equational theories. Specifically, we discuss the existence of tensors, which are combinations of theories that impose mutual commutation of the operations from the…

In this paper, a problem of testing is discussed when the samples have been drawn from the normal distribution. The study of hypothesis testing is also extended to Baye's set up.

We show that the local-global divisibility in commutative algebraic groups defined over number fields can be tested on sets of primes of arbitrary small density, i.e. stable and persistent sets. We also give a new description of the…

We classify the twisted tensor products of a finite set algebra with a two elements set algebra using colored quivers obtained through considerations analogous to Ore extensions. This provides also a classification of entwining structures…

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…

We exhibit a map f between aspherical spaces X and Y such that f induces an isomorphism on homotopy groups but, with natural topologies, X and Y fail to have homeomorphic fundamental groups. Thus the topological fundamental group has the…

We follow the dual approach to Coxeter systems and show for Weyl groups a criterium which decides whether a set of reflections is generating the group depending on the root and the coroot lattice. Further we study special generating sets…

In this paper we provide descriptions of the Whitehead groups with coefficients in a ring of the Hilbert modular group and its reduced version, as well as for the topological K-theory of $C^*$-algebras, after tensoring with $\mathbb{Q}$, by…

Several approaches to testing the hypothesis that two histograms are drawn from the same distribution are investigated. We note that single-sample continuous distribution tests may be adapted to this two-sample grouped data situation. The…

The sun dual space corresponding to a strongly continuous semigroup is a known concept when dealing with dual semigroups, which are in general only weak$^*$-continuous. In this paper we develop a corresponding theory for bi-continuous…

We review the interpretation of Whitehead products in homotopy theory as an entanglement of topological defects in ordered media.

We consider the problem of hypothesis testing in the situation when the first hypothesis is simple and the second one is local one-sided composite. We describe the choice of the thresholds and the power functions of the Score Function test,…

A 2-group is a `categorified' version of a group, in which the underlying set G has been replaced by a category and the multiplication map m: G x G -> G has been replaced by a functor. A number of precise definitions of this notion have…

We study and develop a notion of isogeny for superstable groups. We prove several fundamental properties of the notion and then use it to formulate and prove uniqueness results. Connections to existing model theoretic notions are explained.

Accurate detection of infected individuals is one of the critical steps in stopping any pandemic. When the underlying infection rate of the disease is low, testing people in groups, instead of testing each individual in the population, can…

We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like ``a random element (or a tuple of elements) of a group G has a…

By use of Siegel's method and the classical results of homotopy groups of spheres and Lie groups, we determine some Gottlieb groups of projective spaces or give the lower bounds of their orders. Furthermore, making use of the properties of…

A quantum field theory with a finite abelian symmetry $G$ may be equipped with a non-invertible duality defect associated with gauging $G$. For certain $G$, duality defects admit an alternative construction where one starts with invertible…