The dual of noncommutative Lorentz spaces

We prove some noncommutative analogues of the classical results about dual spaces of the classical Lorentz spaces.     

Towers of Corings

Abstract

The notion of a Frobenius coring is introduced, and it is shown that any such coring produces a Jones-like tower of Frobenius corings and Frobenius extensions. This establishes a one-to-one correspondence between Frobenius corings and extensions.     

The Canonical Basis for the Quantum Group of Type B2

We use the Ringel-Hall algebra approach to study the canonical basis elements for the quantum group of type B₂ which are characterized in Xi [12]. However, our approach simplifies several computations there.     

The K-Theory of Cuntz–Krieger Algebras for Infinite Matrices

We compute the K-theory groups of the Cuntz–Krieger C^*-algebra O_A associated to an infinite matrix A of zeros and ones.     

Homological Algebra for Coalgebraic Modules and Mod p K-Theory of Infinite Loop Spaces

In this paper, we develop the theory of homological algebra for coalgebraic modules, and compute and p K-theory of infinite loop spaces associated to BP-module spectra.     

Geometric structure of dimension functions of certain continuous fields

For a continuous field of C^?-algebras A, we give a criterion to ensure that the stable rank of A is one. In the particular case of a trivial field this leads to a characterization of stable rank one, completing accomplishments by Nagisa, Osaka and Phillips. Further, for certain continuous fields of C^?-algebras, we study when the Cuntz semigroup satisfies the Riesz interpolation property, and we also analyze the structure of its functionals. As an application, we obtain a positive answer to a conjecture posed by Blackadar and Handelman in a variety of situations.     

PFI代数及其P滤子

文「１」引入了ＦＩ代数及其滤子,文「２」讨论了ＦＩ代数与ＭＶ代数的联系,本文在此基础上引入了正关联ＦＩ代数及其正关联滤子,并得到几个重要性质。     

Characteristic tilting modules and Ringel duals

The characteristic tilting modules of quasi-hereditary algebras which are dual extensions of directed monomial algebras are explicitly constructed; and it is shown that the Ringel dual of the dual extension of an arbitrary hereditary algebra has triangular decomposition and bipartite quiver.     

Nonlinear generalized sections and vector bundle homomorphisms in Colombeau spaces of generalized functions

We define and characterize spaces of manifold‐valued generalized functions and generalized vector bundle homomorphisms in the setting of the full diffeomorphism‐invariant vector‐valued Colombeau algebra. Furthermore, we establish point value characterizations for these spaces.