In this paper we present algebraic constructions of 3×3, 4× 4 and 6 × 6 Space-Time Codes, achieving full rate and full diversity. These codes have non-vanishing (in fact fixed) minimum determinants when the rate goes to infinity. Their construction is based on cyclic algebras with center equal to an algebraic field based on cyclotomic fields .

This paper describes all the identities of degree 7 satisfied by algebras of 2 × 2 matrices over the octonions. There are three cases: (1) the full matrix algebra under the usual matrix product, (2) the algebra of Hermitian matrices under the symmetric product, and (3) the algebra of skewHermitian matrices under the antisymmetric product. In case (1) we present seven new identities in degree 7 ...

The dually conjugate Hopf algebras Funp,q(R) and Up,q(R) associated with the two-parametric (p, q)-Alexander-Conway solution (R) of the Yang-Baxter equation are studied. Using the Hopf duality construction, the full Hopf structure of the quasitriangular enveloping algebra Up,q(R) is extracted. The universal T matrix for Funp,q(R) is derived. While expressing an arbitrary group element of the qu...

We formulate the Hopf algebra underlying the su(2|2) S-matrix relevant for the AdS/CFT correspondence, extending the one discovered by Janik in the su(1|2) sector to the full algebra, by specifying the action of the coproduct and the antipode on the remaining generators. The nontriviality of the coproduct is determined by the lenght-changing effect, and results in an unusual central braiding. W...

Arveson's extension theorem guarantees that every completely positive map defined on an operator system can be extended to a the whole C*-algebra containing it. An analogous statement where complete positivity is replaced by known false. A natural question whether extendibility could still hold for maps satisfying stronger conditions, such as being unital and norm 1. Here we provide three count...

The full Kostant–Toda hierarchy on a semisimple Lie algebra is system of Lax equations, in which the flows are determined by gradients Chevalley invariants. This paper concerned with even orthogonal algebra. By using Pfaffian matrix as one invariants, we construct an explicit form flow associated to this invariant. As main result, introduce extension Schur’s Q-functions time variables, and use ...

several representations of the generalized drazin inverse of an anti-triangular block matrix in banach algebra are given in terms of the generalized banachiewicz--schur form.