We construct a differential and a Lie bracket on the space {Hom(A, A)},k,l≥0 for any associative algebra A. The restriction of this bracket to the space {Hom(A, A)},k≥0 is exactly the Gerstenhaber bracket. We discuss some formality conjecture related with this construction. We also discuss some applications to deformation theory. 0. There exists a well-known way (due to Jim Stasheff) to define ...

We study isomorphism classes of symplectic dual pairs P ← S → P , where P is an integrable Poisson manifold, S is symplectic, and the two maps are complete, surjective Poisson submersions with connected and simply-connected fibres. For fixed P , these Morita self-equivalences of P form a group Pic(P ) under a natural “tensor product” operation. Variants of this construction are also studied, fo...

This paper presents experimental results of a coverage analysis in a WCDMA network using the 850 MHz band; an urban electromagnetic propagation environment is considered. Obtained coverage estimation maps are based on Krige statistical method of interpolation. Key performance parameters used in this work are the CPICH and Ec. The results could be used to identify problems and help to optimize c...

We define the operation of Petrie duality for maps, describing its general properties both geometrically and algebraically. We give a number of examples and applications, including the construction of a pair of regular maps, one orientable of genus 17, the other non-orientable of genus 52, which embed the 40-vertex cage of valency 6 and girth 5 discovered independently by Robertson and Anstee. ...

We prove that every element of the polar cone to the closed convex cone of monotone transport maps can be represented as the divergence of a measure field taking values in the positive definite matrices.

We generalize the main theorem of Rieffel for Morita equivalence of W -algebras to the case of unital dual operator algebras: two unital dual operator algebras A,B have completely isometric normal representations α, β such that α(A) = [Mβ(B)M] ∗ and β(B) = [Mα(A)M] ∗ for a ternary ring of operators M (i.e. a linear space M such that MMM ⊂ M) if and only if there exists an equivalence functor F ...

The notion of separable (alternatively unramified, or decidable) objects and their place in a categorical theory of space have been described by Lawvere (see [9]), drawing on notions of separable from algebra and unramified from geometry. In [10], Schanuel constructed the generic separable object in an extensive category with products as an object of the free category with finite sums on the du...

In this paper,we consider a parametric generalized vector quasiequilibriumproblemwhich is mixed in the sense that several different relations can simultaneously appear in this problem. The moving cones and other data of the problem are assumed to be set-valued maps defined in topological spaces and taking values in topological spaces or topological vector spaces. The main result of this paper g...

We investigate some subtle and interesting phenomena in the du-ality theory of operator spaces and operator algebras. In particular, we give several applications of operator space theory, based on the surprising fact that certain maps are always weak *-continuous on dual operator spaces. For example , if X is a subspace of a C *-algebra A, and if a ∈ A satisfies aX ⊂ X and a * X ⊂ X, and if X i...

Let (A, ∆) be a multiplier Hopf algebra. In general, the underlying algebra A need not have an identity and the coproduct ∆ does not map A into A ⊗ A but rather into its multiplier algebra M (A ⊗ A). In this paper, we study some tools that are frequently used when dealing with such multiplier Hopf algebras and that are typical for working with algebras without identity in this context. The basi...