On nonassociative division algebras

On Nonassociative Division Algebras^)

Nonassociative Algebras

Space-time block codes from nonassociative division algebras

Space-time coding is used for reliable high rate transmission over wireless digital channels with multiple antennas at both the transmitter and receiver ends. From a mathematical point of view, a space-time block code (STBC) consists of a family of matrices with complex entries (the codebook) that satisfies a number of properties which determine how well the code performs. The first aim is to f...

A class of nonassociative algebras

A large class of nonassociative algebras, out of the Lie algebras has been studied, often with geometrical structures and sometimes on fondamental spaces as the spaces of Hochschild cohomology. In this paper, we propose to consider all these nonassociative algebras as algebras defined by the action of invariant subspaces of the symmetric group Σ 3 on the associator of the considered laws.

Nonassociative Algebras with Submultiplicative Bilinear Form

In this paper algebras with identity, over ordered fields, which possess a (weak) submultiplicative positive bilinear form are studied. They are called (weak) subdecomposition algebras. It is proved that every weak subdecomposition algebra is a simple quadratic algebra with no nontrivial nilpotents or idempotents. If a weak subdecomposition algebra is also flexible, then it is a noncommutative ...