The topological filtration on the Grothendieck group of the Severi-Brauer variety corresponding to a triquaternion algebra is computed. In particular, it is shown that the second Chow group of the variety is torsionfree. Let F be a field, A a central simple F -algebra of degree 8 and exponent 2, X = SB(A) the Severi-Brauer variety of A [2]. Consider the second Chow group CH(X), i.e. the group o...

Algebraic topology is a young subject, and its foundations are not yet firmly in place. I shall give some history, examples, and modern developments in that part of the subject called stable algebraic topology, or stable homotopy theory. This is by far the most calculationally accessible part of algebraic topology, although it is also the least intuitively grounded in visualizable geometric obj...

It is argued that the geometric dual of a noncommutative operator algebra represents a notion of quantum state space which differs from existing notions by representing observables as maps from states to outcomes rather than from states to distributions on outcomes. A program of solving for an explicitly geometric manifestation of quantum state space by adapting the spectral presheaf, a constru...

A concrete model of computation for a topological algebra is based on a representation of the algebra made from functions on the natural numbers. The functions computable in a concrete model are computable in the representation in the classical sense of the Chruch-Turing Thesis. Moreover, the functions turn out to be continuous in the topology of the algebra. In this paper we consider different...

* Correspondence: [email protected] Department of Mathematics, Tianjin University, Tianjin, 300072 People’s Republic of China Abstract In this paper, we investigate the compactness of the sum of weighted composition operators on the unit ball algebra, and give the characterization of compact differences of two weighted composition operators on the ball algebra. The connectness of the t...

Increasing the expressiveness of qualitative spatial calculi is an essential step towards meeting the requirements of applications. This can be achieved by combining existing calculi in a way that we can express spatial information using relations from multiple calculi. The great challenge is to develop reasoning algorithms that are correct and complete when reasoning over the combined informat...

Let X be an infinite compact metrizable space, and let σ : X → X be a minimal homeomorphism. Suppose that (X,σ) has zero mean topological dimension. The associated C*algebra A = C(X) oσ Z is shown to absorb the Jiang-Su algebra Z tensorially, i.e., A ∼= A⊗ Z. This implies that A is classifiable when (X,σ) is uniquely ergodic. Moreover, without any assumption on the mean dimension, it is shown t...

A family of algebras, which we call topological conjugacy algebras, is associated with each proper continuous map on a locally compact Hausdorff space. Assume that ηi : Xi → Xi is a continuous proper map on a locally compact Hausdorff space Xi, for i = 1, 2. We show that the dynamical systems (X1, η1) and (X2, η2) are conjugate if and only if some topological conjugacy algebra of (X1, η1) is is...

In this article, we formulate a planar limited version of the B-side in homological mirror symmetry that formularizes Chern-Simons-type topological open string field theory using homotopy associative algebra (A∞ algebra). This formulation is based on the works by Dijkgraaf and Vafa. We show that our formularization includes gravity/gauge theory correspondence which originates in the AdS/CFT dua...

A simply connected topological space X has homotopy Lie algebra ( X) Q. Following Quillen, there is a connected di erential graded free Lie algebra (dgL) called a Lie model, which determines the rational homotopy type of X , and whose homology is isomorphic to the homotopy Lie algebra. We show that such a Lie model can be replaced with one that has a special property we call separated. The homo...