Noncommutative Spherical Tight Frames in finitely generated Hilbert C*-modules

Strong Morita equivalence of higher-dimensional noncommutative tori. II

We show that two C*-algebraic noncommutative tori are strongly Morita equivalent if and only if they have isomorphic ordered K_0-groups and centers, extending N. C. Phillips's result in the case that the algebras are simple. This is also generalized to the twisted group C*-algebras of arbitrary finitely generated abelian groups.

Noncommutative correspondence categories, simplicial sets and pro $C^*$-algebras

We show that a $KK$-equivalence between two unital $C^*$-algebras produces a correspondence between their DG categories of finitely generated projective modules which is a $\mathbf{K}_*$-equivalence, where $\mathbf{K}_*$ is Waldhausen's $K$-theory. We discuss some connections with strong deformations of $C^*$-algebras and homological dualities. Motivated by a construction of Cuntz we associate a pro $C^*$-algebra to any simplicial set. We show that this construction is functorial with respect to proper maps of simplicial sets, that we define, and also respects proper homotopy equivalences. We …

Chern numbers for two families of noncommutative Hopf fibrations

We consider noncommutative line bundles associated with the Hopf fibrations of SUq(2) over all Podles spheres and with a locally trivial Hopf fibration of S^3_{pq}. These bundles are given as finitely generated projective modules associated via 1-dimensional representations of U(1) with Galois-type extensions encoding the principal fibrations of SUq(2) and S^3_{pq}. We show that the Chern numbers of these modules coincide with the winding numbers of representations defining them.

非交换代数中的增长与导出范畴中的熵

Growth in noncommutative algebras and entropy in derived categories

本文通过Serre扭转函子的范畴熵和多项式熵，建立了非交换射影簇的维数类比，并证明了这些熵与代数增长及Gelfand-Kirillov维数的关系。

单项式代数的熵与导出范畴

Entropy of monomial algebras and derived categories

该研究针对有限表现结合单项式代数，计算其导出范畴上Serre扭函子的范畴熵，证明其等于代数自身熵的对数，并建立了与Ufnarovski图拓扑熵、路代数熵及箭图邻接矩阵谱半径的关联。