arXiv subjects
Publications and source records attributed to Hanfeng Li.
We show that matrices in the same orbit of the SO(n, n|Z) action on the space of n\times n skew-symmetric matrices give strong Morita equivalent noncommutative tori, both at the C*-algebra level and at the smooth algebra level. This proves a conjecture of Rieffel and Schwarz.
We construct explicitly some analytic families of etale (phi,Gamma)-modules, which give rise to analytic families of 2-dimensional crystalline representations. As an application of our constructions, we verify some conjectures of Breuil on the reduction modulo p of those representations, and extend some results (of Deligne, Edixhoven, Fontaine and Serre) on the representations arising from modular forms.
We characterize positive topological entropy for quasi-state space homeomorphisms induced from $C^*$-algebra automorphisms in terms of dynamically generated subspaces isomorphic to $\ell_1$. This geometric condition is also used to give a description of the topological Pinsker algebra. In particular we obtain a geometric characterization of positive entropy for topological dynamical systems, as well as an analogue for completely positive topological entropy of Glasner and Weiss's combinatorial characterization of completely positive Kolmogorov-Sinai entropy.
We show that the Voiculescu-Brown entropy of a noncommutative toral automorphism arising from a matrix S in GL(d,Z) is at least half the value of the topological entropy of the corresponding classical toral automorphism. We also obtain some information concerning the positivity of local Voiculescu-Brown entropy with respect to single unitaries. In particular we show that if S has no roots of unity as eigenvalues then the local Voiculescu-Brown entropy with respect to every product of canonical unitaries is positive, and also that in the presence of completely positive CNT entropy the unital version of local Voiculescu-Brown entropy with respect to every non-scalar unitary is positive.
We examine the question of when the *-homomorphism of full amalgamated free product C*-algebras λ: A *_D B --> A' *_{D'} B', arising from compatible inclusions of C*-algebras A in A', B in B' and D in D', is an embedding. Results giving sufficient conditions for λto be injective, as well of classes of examples where λfails to be injective, are obtained. As an application, we give necessary and sufficient condition for the full amalgamated free product of finite dimensional C*-algebras to be residually finite dimensional.