Leopardi introduced the notion of a Kronecker quotient in [Paul Leopardi. A generalized FFT for Clifford algebras. Bulletin of the Belgian Mathematical Society, 11:663–688, 2005.]. This article considers the basic properties that a Kronecker quotient should satisfy and additional properties which may be satisfied. A class of Kronecker quotients for which these properties have a natural descript...

We give a proof using so-called fusion rings and q-deformations of Brauer algebras that the representation ring of an orthogonal or symplectic group can be obtained as a quotient of a ring Gr(O(∞)). This is obtained here as a limiting case for analogous quotient maps for fusion categories, with the level going to ∞. This in turn allows a detailed description of the quotient map in terms of a re...

We consider closed topological 4-manifolds M with universal cover S × S and Euler characteristic χ(M) = 1. All such manifolds with π = π1(M) ∼= Z/4 are homotopy equivalent. In this case, we show that there are four homeomorphism types, and propose a candidate for a smooth example which is not homeomorphic to the geometric quotient. If π ∼= Z/2×Z/2, we show that there are three homotopy types (a...

This paper presents an algorithm for the Quillen-Suslin Theorem for quotients of polynomial rings by monomial ideals, that is, quotients of the form A = kx 0 ; :::;xn]=I, with I a monomial ideal and k a eld. T. Vorst proved that nitely generated projective modules over such algebras are free. Given a nitely generated module P, described by generators and relations, the algorithm tests whether P...

For an irrational number x, let xn denote its n-th continued fraction inverse complete quotient, obtained by deleting the first n partial quotients. For any positive real number r, we establish the optimal linear bound on the sum of the r-th powers of the first n complete quotients. That is, we find the smallest constants α(r),β(r) such that x1 + . . . + x r n < α(r)n + β(r) for all n ≥ 1 and a...

In this paper we consider five possible extensions of the Prüfer domain notion to the case of commutative rings with zero divisors and relate the corresponding properties on a ring with the property of its total ring of quotients. We show that a Prüfer ring R satisfies one of the five conditions if and only if the total ring of quotients Q(R) of R satisfies that same condition. We focus in part...

We extend the notion of exact completion on a category with weak finite limits to Lawvere’s elementary doctrines. We show how any such doctrine admits an elementary quotient completion, which is the universal solution to adding certain quotients. We note that the elementary quotient completion can be obtained as the composite of two other universal constructions: one adds effective quotients, t...

We establish a description of the maximal C*-algebra of quotients of a unital C*-algebra A as a direct limit of spaces of completely bounded bimodule homomorphisms from certain operator submodules of the Haagerup tensor product A ⊗h A labelled by the essential closed right ideals of A into A. In addition the invariance of the construction of the maximal C*-algebra of quotients under strong Mori...

We study the existence of cubic quotients of finite-dimensional quasi-normed spaces, that is, quotients well isomorphic to `∞ for some k. We give two results of this nature. The first guarantees a proportional dimensional cubic quotient when the envelope is cubic; the second gives an estimate for the size of a cubic quotient in terms of a measure of nonconvexity of the quasi-norm.

In a recent paper, Stasinski and Voll introduced a length-like statistic on hyperoctahedral groups and conjectured a product formula for this statistic’s signed distribution over arbitrary descent classes. Stasinski and Voll proved this conjecture for a few special types of parabolic quotients. We prove this conjecture in full, showing it holds for all parabolic quotients. In the case that the ...