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Register a new userMorita equivalence and characteristic classes of star products
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This paper deals with two aspects of the theory of characteristic classes of star products: first, on an arbitrary Poisson manifold, we describe Morita equivalent star products in terms of their Kontsevich classes; second, on symplectic manifolds, we describe the relationship between Kontsevichs and Fedosovs characteristic classes of star products.
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We construct cup products of two different kinds for Hopf-cyclic cohomology. When the Hopf algebra reduces to the ground field our first cup product reduces to Connes cup product in ordinary cyclic cohomology. The second cup product generalizes Connes-Moscovicis characteristic map for actions of Hopf algebras on algebras.
Logicians and philosophers of science have proposed various formal criteria for theoretical equivalence. In this paper, we examine two such proposals: definitional equivalence and categorical equivalence. In order to show precisely how these two well-known criteria are related to one another, we investigate an intermediate criterion called Morita equivalence.
This note proves that, as K-theory elements, the symbol classes of the de Rham operator and the signature operator on a closed manifold of even dimension are congruent mod 2. An equivariant generalization is given pertaining to the equivariant Euler characteristic and the multi-signature.
Morita equivalence of twisted inverse semigroup actions and discrete twisted partial actions are introduced. Morita equivalent actions have Morita equivalent crossed products.
Let $C$ be a unital AH-algebra and $A$ be a unital simple C*-algebra with tracial rank zero. It has been shown that two unital monomorphisms $phi, psi: Cto A$ are approximately unitarily equivalent if and only if $$ [phi]=[psi] {rm in} KL(C,A) and taucirc phi=taucirc psi tforal tauin T(A), $$ where $T(A)$ is the tracial state space of $A.$ In this paper we prove the following: Given $kappain KL(C,A)$ with $kappa(K_0(C)_+setminus {0})subset K_0(A)_+setminus {0}$ and with $kappa([1_C])=[1_A]$ and a continuous affine map $lambda: T(A)to T_{mathtt{f}}(C)$ which is compatible with $kappa,$ where $T_{mathtt{f}}(C)$ is the convex set of all faithful tracial states, there exists a unital monomorphism $phi: Cto A$ such that $$ [phi]=kappaandeqn taucirc phi(c)=lambda(tau)(c) $$ for all $cin C_{s.a.}$ and $tauin T(A).$ Denote by ${rm Mon}_{au}^e(C,A)$ the set of approximate unitary equivalence classes of unital monomorphisms. We provide a bijective map $$ Lambda: {rm Mon}_{au}^e (C,A)to KLT(C,A)^{++}, $$ where $KLT(C,A)^{++}$ is the set of compatible pairs of elements in $KL(C,A)^{++}$ and continuous affine maps from $T(A)$ to $T_{mathtt{f}}(C).$ Moreover, we realized that there are compact metric spaces $X$, unital simple AF-algebras $A$ and $kappain KL(C(X), A)$ with $kappa(K_0(C(X))_+setminus{0})subset K_0(A)_+setminus {0}$ for which there is no hm $h: C(X)to A$ so that $[h]=kappa.$
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