We propose in this paper a new highly scalable key management scheme for WSN. We make use, for the first time, of the unital design theory for key pre-distribution in WSN. We propose a naive mapping from unitals to key pre-distribution as well as an enhanced unital-based key management scheme. We analyze our solution and compare it to basic approaches; results show that our scheme enhances cons...

Let U be a known unital of PG(2, q), q odd, and let N be a t-nest in a regular spread S. Suppose we replace N by a replacement set N̂ to form the new spread S ′ = (S\N)∪ N̂ ). Using the Bruck-Bose correspondence, we look at the affine points of U in P(S) ∼= PG(2, q) and see whether the corresponding affine point set in the new plane P(S ′) can be completed to a unital.

We give a classification theorem for unital separable nuclear simple C∗-algebras with tracial rank no more than one. Let A and B be two unital separable simple nuclear C∗-algebras with TR(A), TR(B) ≤ 1 which satisfy the universal coefficient theorem. We show that A ∼= B if and only if (K0(A),K0(A)+, [1A], K1(A), T (A)) ∼= (K0(B), K0(B)+, [1B ], K1(B), T (B)).

We consider algebras over a field k of characteristic zero. The article is concerned with the isomorphism of graded vectorspaces H(gl(A)) ∼ → ∧(HC(A)[−1]) between the Lie algebra homology of matrices and the free graded commutative algebra on the cyclic homology of the k-algebra A, shifted down one degree. For unital algebras this isomorphism is a classical result obtained by Loday and Quillen ...

In this note, unless we say otherwise every vector space or algebra we speak about is over C. If A is a Banach algebra and e ∈ A satisfies xe = x and ex = x for all x ∈ A, and also ‖e‖ = 1, we say that e is unity and that A is unital. If A is a unital Banach algebra and x ∈ A, the spectrum of x is the set σ(x) of those λ ∈ C for which λe−x is not invertible. It is a fact that if A is a unital B...

We introduce the notion of locally finite decomposition rank, a structural property shared by many stably finite nuclear C∗-algebras. The concept is particularly relevant for Elliott’s program to classify nuclear C∗algebras by K-theory data. We study some of its properties and show that a simple unital C∗-algebra, which has locally finite decomposition rank, real rank zero and which absorbs the...

Conditions sufficient for a quantum dynamical semigroup (QDS) to be unital are proved for a class of problems in quantum optics with Hamiltonians which are self-adjoint polynomials of any finite order in creation and annihilation operators. The order of the Hamiltonian may be higher than the order of completely positive part of the formal generator of a QDS. The unital property of a minimal qua...

Let A be an algebra over a commutative unital ring C. We say that A is zero triple product determined if for every C-module X and every trilinear map {·, ·, ·}, the following holds: if {x, y, z} 0 whenever xyz 0, then there exists a C-linear operator T : A3 −→ X such that {x, y, z} T xyz for all x, y, z ∈ A. If the ordinary triple product in the aforementioned definition is replaced by Jordan t...

Let B be a σ–unital C–algebra. We show that every strongly continuous E0–semigroup on the algebra of adjointable operators on a full Hilbert B–module E gives rise to a full continuous product system of correspondences over B. We show that every full continuous product system of correspondences over B arises in that way. If the product system is countably generated, then E can be chosen countabl...