Jones index theory for Hilbert C*-bimodules and its equivalence with conjugation theory

We introduce the notion of finite right (respectively left) numerical index on a bimodule $X$ over C*-algebras A and B with a bi-Hilbertian structure. This notion is based on a Pimsner-Popa type inequality. The right (respectively left) index element of X can be constructed in the centre of the enveloping von Neumann algebra of A (respectively B). X is called of finite right index if the right index element lies in the multiplier algebra of A. In this case we can perform the Jones basic construction. Furthermore the C*--algebra of bimodule mappings with a right adjoint is a continuous field of finite dimensional C*-algebras over the spectrum of Z(M(A)), whose fiber dimensions are bounded above by the index. We show that if A is unital, the right index element belongs to A if and only if X is finitely generated as a right module. We show that bi-Hilbertian, finite (right and left) index C*-bimodules are precisely those objects of the tensor 2-C*-category of right Hilbertian C*-bimodules with a conjugate object, in the sense of Longo and Roberts, in the same category.Comment: 59 pages, amste

KMS States, Entropy and the Variational Principle in full C*-dynamical systems

To any periodic, unital and full C*-dynamical system (A, \alpha, R) an invertible operator s acting on the Banach space of trace functionals of the fixed point algebra is canonically associated. KMS states correspond to positive eigenvectors of s. A Perron-Frobenius type theorem asserts the existence of KMS states at inverse temperatures equal the logarithms of the inner and outer spectral radii of s (extremal KMS states). Examples arising from subshifts in symbolic dynamics, self-similar sets in fractal geometry and noncommutative metric spaces are discussed. Certain subshifts are naturally associated to the system and the relationship between their topological entropy and inverse temperatures of extremal KMS states are given. Noncommutative shift maps are considered. It is shown that their entropy is bounded by the sum of the entropy of the associated subshift and a suitable entropy computed in the homogeneous subalgebra. Examples are discussed among Matsumoto algebras associated to certain non finite type subshifts. The CNT entropy is compared to the classical measure-theoretic entropy of the subshift. A noncommutative analogue of the classical variational principle for the entropy of subshifts is obtained for the noncommutative shift of certain Matsumoto algebras. More generally, a necessary condition is discussed. In the case of Cuntz-Krieger algebras an explicit construction of the state with maximal entropy from the unique KMS state is done.Comment: 52 pages, AMSTeX. An error in Prop. 7.3 v1 has been corrected, and related text in sections 7-9 has been modified. References added. Abstract modifie

Invariant subspace theorems for subdiagonal algebras

We investigate a certain class of invariant subspaces of subdiagonal algebras which contains the both cases of (extended) weak-*Dirichle algebras and analytic crossed products. We show a version of the Beurling-Lax-Halmos theorem

On Property (FA) for wreath products

We characterize permutational wreath products with Property (FA). For instance, the standard wreath product A wr B of two nontrivial countable groups A,B, has Property (FA) if and only if B has Property (FA) and A is a finitely generated group with finite abelianisation. We also prove an analogous result for hereditary Property (FA). On the other hand, we prove that many wreath products with hereditary Property (FA) are not quotients of finitely presented groups with the same property.Comment: 12 pages, 0 figur

Maternal lineages in polyploid wheat species inferred from organeller DNA fingerprinting

Contains fulltext : 134958.pdf (publisher's version ) (Closed access)Health promoting messages can be framed in terms of the gains that are associated with healthy behaviour, or the losses that are associated with unhealthy behaviour. In this study, we examined the influence of self-efficacy to quit smoking on the effects of gain framed and loss framed anti-smoking messages in a randomized controlled trial among 539 adult smokers. Participants with a high self-efficacy to quit smoking reported higher levels of motivation to quit smoking after receiving a loss framed message than after receiving a gain framed message or no message. For these participants receiving a gain framed message did not result in a higher motivation to quit smoking than receiving no message. For participants with a low self-efficacy to quit smoking there were no differences in motivation to quit smoking between the gain framed message condition, loss framed message condition and control condition. Our results suggest that self-efficacy can moderate the effects of message framing on persuasion

Exploration of finite dimensional Kac algebras and lattices of intermediate subfactors of irreducible inclusions

We study the four infinite families KA(n), KB(n), KD(n), KQ(n) of finite dimensional Hopf (in fact Kac) algebras constructed respectively by A. Masuoka and L. Vainerman: isomorphisms, automorphism groups, self-duality, lattices of coideal subalgebras. We reduce the study to KD(n) by proving that the others are isomorphic to KD(n), its dual, or an index 2 subalgebra of KD(2n). We derive many examples of lattices of intermediate subfactors of the inclusions of depth 2 associated to those Kac algebras, as well as the corresponding principal graphs, which is the original motivation. Along the way, we extend some general results on the Galois correspondence for depth 2 inclusions, and develop some tools and algorithms for the study of twisted group algebras and their lattices of coideal subalgebras. This research was driven by heavy computer exploration, whose tools and methodology we further describe.Comment: v1: 84 pages, 13 figures, submitted. v2: 94 pages, 15 figures, added connections with Masuoka's families KA and KB, description of K3 in KD(n), lattices for KD(8) and KD(15). v3: 93 pages, 15 figures, proven lattice for KD(6), misc improvements, accepted for publication in Journal of Algebra and Its Application